diff --git a/src/problems/problem_utils.jl b/src/problems/problem_utils.jl
index 3c10f5fdf..f2faaf20b 100644
--- a/src/problems/problem_utils.jl
+++ b/src/problems/problem_utils.jl
@@ -180,3 +180,6 @@ function Base.summary(io::IO, prob::AbstractPDEProblem)
 end
 
 Base.copy(p::SciMLBase.NullParameters) = p
+
+SymbolicIndexingInterface.is_time_dependent(::AbstractDEProblem) = true
+SymbolicIndexingInterface.is_time_dependent(::AbstractNonlinearProblem) = false
diff --git a/src/remake.jl b/src/remake.jl
index dac9c3e12..73d7634ef 100644
--- a/src/remake.jl
+++ b/src/remake.jl
@@ -257,18 +257,9 @@ function remake(prob::ODEProblem; f = missing,
         ODEProblem{iip}(f, newu0, tspan, newp, prob.problem_type; kwargs...)
     end
 
-    if lazy_initialization === nothing
-        lazy_initialization = !is_trivial_initialization(initialization_data)
-    end
-    if initialization_data !== nothing && !lazy_initialization
-        u0, p, _ = get_initial_values(
-            prob, prob, prob.f, OverrideInit(), Val(isinplace(prob)))
-        if u0 !== nothing && eltype(u0) == Any && isempty(u0)
-            u0 = nothing
-        end
-        @reset prob.u0 = u0
-        @reset prob.p = p
-    end
+    u0, p = maybe_eager_initialize_problem(prob, initialization_data, lazy_initialization)
+    @reset prob.u0 = u0
+    @reset prob.p = p
 
     return prob
 end
@@ -453,18 +444,10 @@ function remake(prob::SDEProblem;
     else
         SDEProblem{iip}(f, newu0, tspan, newp; noise, noise_rate_prototype, seed, kwargs...)
     end
-    if lazy_initialization === nothing
-        lazy_initialization = !is_trivial_initialization(initialization_data)
-    end
-    if initialization_data !== nothing && !lazy_initialization
-        u0, p, _ = get_initial_values(
-            prob, prob, prob.f, OverrideInit(), Val(isinplace(prob)))
-        if u0 !== nothing && eltype(u0) == Any && isempty(u0)
-            u0 = nothing
-        end
-        @reset prob.u0 = u0
-        @reset prob.p = p
-    end
+
+    u0, p = maybe_eager_initialize_problem(prob, initialization_data, lazy_initialization)
+    @reset prob.u0 = u0
+    @reset prob.p = p
 
     return prob
 end
@@ -520,18 +503,10 @@ function remake(prob::DDEProblem; f = missing, h = missing, u0 = missing,
         DDEProblem{iip}(f, newu0, h, tspan, newp; constant_lags, dependent_lags,
             order_discontinuity_t0, neutral, kwargs...)
     end
-    if lazy_initialization === nothing
-        lazy_initialization = !is_trivial_initialization(initialization_data)
-    end
-    if initialization_data !== nothing && !lazy_initialization
-        u0, p, _ = get_initial_values(
-            prob, prob, prob.f, OverrideInit(), Val(isinplace(prob)))
-        if u0 !== nothing && eltype(u0) == Any && isempty(u0)
-            u0 = nothing
-        end
-        @reset prob.u0 = u0
-        @reset prob.p = p
-    end
+
+    u0, p = maybe_eager_initialize_problem(prob, initialization_data, lazy_initialization)
+    @reset prob.u0 = u0
+    @reset prob.p = p
 
     return prob
 end
@@ -619,18 +594,9 @@ function remake(prob::SDDEProblem;
             dependent_lags, order_discontinuity_t0, neutral, kwargs...)
     end
 
-    if lazy_initialization === nothing
-        lazy_initialization = !is_trivial_initialization(initialization_data)
-    end
-    if initialization_data !== nothing && !lazy_initialization
-        u0, p, _ = get_initial_values(
-            prob, prob, prob.f, OverrideInit(), Val(isinplace(prob)))
-        if u0 !== nothing && eltype(u0) == Any && isempty(u0)
-            u0 = nothing
-        end
-        @reset prob.u0 = u0
-        @reset prob.p = p
-    end
+    u0, p = maybe_eager_initialize_problem(prob, initialization_data, lazy_initialization)
+    @reset prob.u0 = u0
+    @reset prob.p = p
 
     return prob
 end
@@ -741,18 +707,9 @@ function remake(prob::NonlinearProblem;
             problem_type = problem_type; kwargs...)
     end
 
-    if lazy_initialization === nothing
-        lazy_initialization = !is_trivial_initialization(initialization_data)
-    end
-    if initialization_data !== nothing && !lazy_initialization
-        u0, p, _ = get_initial_values(
-            prob, prob, prob.f, OverrideInit(), Val(isinplace(prob)))
-        if u0 !== nothing && eltype(u0) == Any && isempty(u0)
-            u0 = nothing
-        end
-        @reset prob.u0 = u0
-        @reset prob.p = p
-    end
+    u0, p = maybe_eager_initialize_problem(prob, initialization_data, lazy_initialization)
+    @reset prob.u0 = u0
+    @reset prob.p = p
 
     return prob
 end
@@ -792,18 +749,9 @@ function remake(prob::NonlinearLeastSquaresProblem; f = missing, u0 = missing, p
             f, u0 = newu0, p = newp, kwargs...)
     end
 
-    if lazy_initialization === nothing
-        lazy_initialization = !is_trivial_initialization(initialization_data)
-    end
-    if initialization_data !== nothing && !lazy_initialization
-        u0, p, _ = get_initial_values(
-            prob, prob, prob.f, OverrideInit(), Val(isinplace(prob)))
-        if u0 !== nothing && eltype(u0) == Any && isempty(u0)
-            u0 = nothing
-        end
-        @reset prob.u0 = u0
-        @reset prob.p = p
-    end
+    u0, p = maybe_eager_initialize_problem(prob, initialization_data, lazy_initialization)
+    @reset prob.u0 = u0
+    @reset prob.p = p
 
     return prob
 end
@@ -1134,6 +1082,23 @@ function process_p_u0_symbolic(prob, p, u0)
     end
 end
 
+function maybe_eager_initialize_problem(prob::AbstractSciMLProblem, initialization_data, lazy_initialization::Union{Nothing, Bool})
+    if lazy_initialization === nothing
+        lazy_initialization = !is_trivial_initialization(initialization_data)
+    end
+    if initialization_data !== nothing && !lazy_initialization && (!is_time_dependent(prob) || current_time(prob) !== nothing)
+        u0, p, _ = get_initial_values(
+            prob, prob, prob.f, OverrideInit(), Val(isinplace(prob)))
+        if u0 !== nothing && eltype(u0) == Any && isempty(u0)
+            u0 = nothing
+        end
+    else
+        u0 = state_values(prob)
+        p = parameter_values(prob)
+    end
+    return u0, p
+end
+
 function remake(thing::AbstractJumpProblem; kwargs...)
     parameterless_type(thing)(remake(thing.prob; kwargs...))
 end
diff --git a/test/initialization.jl b/test/initialization.jl
index 1bf5886f5..e52b3c80c 100644
--- a/test/initialization.jl
+++ b/test/initialization.jl
@@ -263,7 +263,10 @@ end
     @testset "Trivial initialization" begin
         initprob = NonlinearProblem(Returns(nothing), nothing, [1.0])
         update_initializeprob! = function (iprob, integ)
-            iprob.p[1] = integ.u[1]
+            # just to access the current time and use it as a number, so this errors
+            # if run on a problem with `current_time(prob) === nothing`
+            iprob.p[1] = current_time(integ) + 1 
+            iprob.p[1] = state_values(integ)[1]
         end
         initprobmap = function (nlsol)
             u1 = parameter_values(nlsol)[1]
@@ -284,6 +287,11 @@ end
         @test u0 ≈ [2.0, 2.0]
         @test p ≈ 0.0
         @test success
+
+        @testset "Doesn't run in `remake` if `tspan == (nothing, nothing)`" begin
+            prob = ODEProblem(fn, [2.0, 0.0], (nothing, nothing), 0.0)
+            @test_nowarn remake(prob)
+        end
     end
 end
 
diff --git a/test/remake_tests.jl b/test/remake_tests.jl
index 3fdf797ff..307c4d871 100644
--- a/test/remake_tests.jl
+++ b/test/remake_tests.jl
@@ -15,6 +15,7 @@ u0 = [1.0; 2.0; 3.0]
 tspan = (0.0, 100.0)
 p = [10.0, 20.0, 30.0]
 sys = SymbolCache([:x, :y, :z], [:a, :b, :c], :t)
+indep_sys = SymbolCache([:x, :y, :z], [:a, :b, :c])
 fn = ODEFunction(lorenz!; sys)
 for T in containerTypes
     push!(probs, ODEProblem(fn, u0, tspan, T(p)))
@@ -64,7 +65,7 @@ function loss(x, p)
     return sum(du)
 end
 
-fn = OptimizationFunction(loss; sys)
+fn = OptimizationFunction(loss; sys = indep_sys)
 for T in containerTypes
     push!(probs, OptimizationProblem(fn, u0, T(p)))
 end
@@ -73,7 +74,7 @@ function nllorenz!(du, u, p)
     lorenz!(du, u, p, 0.0)
 end
 
-fn = NonlinearFunction(nllorenz!; sys)
+fn = NonlinearFunction(nllorenz!; sys = indep_sys)
 for T in containerTypes
     push!(probs, NonlinearProblem(fn, u0, T(p)))
 end