For end user applications, I usually provide a script that performs the package compiler step as part of “installation”.
I did some analysis of the loading time for these two packages for you.
julia> @time @time_imports using OrdinaryDiffEq, Symbolics
1.5 ms DocStringExtensions
0.3 ms Reexport
0.1 ms SuiteSparse
0.2 ms Requires
2.6 ms ArrayInterface
3.5 ms StaticArraysCore
0.4 ms ArrayInterface → ArrayInterfaceStaticArraysCoreExt
17.9 ms FunctionWrappers
0.4 ms MuladdMacro
9.4 ms OrderedCollections
0.3 ms UnPack
0.4 ms Parameters
0.9 ms Statistics
0.1 ms IfElse
33.1 ms Static
0.3 ms Compat
0.2 ms Compat → CompatLinearAlgebraExt
16.8 ms Preferences
0.3 ms SnoopPrecompile
6.8 ms StaticArrayInterface
1.4 ms ManualMemory
49.0 ms ThreadingUtilities
0.3 ms SIMDTypes
5.1 ms LayoutPointers
5.1 ms CloseOpenIntervals
441.1 ms StrideArraysCore
0.3 ms BitTwiddlingConvenienceFunctions
0.9 ms CpuId
153.6 ms CPUSummary 95.26% compilation time
7.2 ms PolyesterWeave
0.8 ms Polyester
0.4 ms FastBroadcast
34.9 ms ChainRulesCore
0.3 ms PrecompileTools
46.6 ms RecipesBase
0.8 ms SymbolicIndexingInterface
0.3 ms Adapt
0.1 ms DataValueInterfaces
1.0 ms DataAPI
0.2 ms IteratorInterfaceExtensions
0.2 ms TableTraits
41.5 ms Tables
2.3 ms GPUArraysCore
0.2 ms ArrayInterface → ArrayInterfaceGPUArraysCoreExt
18.5 ms RecursiveArrayTools
12.2 ms MacroTools
0.3 ms TruncatedStacktraces
0.8 ms ZygoteRules
1.2 ms ConstructionBase
21.0 ms Setfield
7.2 ms IrrationalConstants
1.1 ms DiffRules
4.1 ms DiffResults
0.2 ms OpenLibm_jll
0.3 ms NaNMath
0.4 ms LogExpFunctions
0.5 ms LogExpFunctions → LogExpFunctionsChainRulesCoreExt
0.3 ms JLLWrappers
5.2 ms OpenSpecFun_jll 87.29% compilation time
14.4 ms SpecialFunctions
1.0 ms SpecialFunctions → SpecialFunctionsChainRulesCoreExt
0.3 ms CommonSubexpressions
82.1 ms ForwardDiff
0.5 ms EnumX
1.2 ms PreallocationTools
0.5 ms FunctionWrappersWrappers
0.2 ms CommonSolve
0.3 ms ExprTools
1.0 ms RuntimeGeneratedFunctions
0.3 ms Tricks
12.9 ms Lazy
18.6 ms SciMLOperators
190.4 ms SciMLBase
8.6 ms DiffEqBase
0.3 ms FastClosures
3.2 ms ArrayInterfaceCore
39.0 ms HostCPUFeatures
280.0 ms VectorizationBase
4.8 ms SLEEFPirates
61.1 ms OffsetArrays
1.3 ms StaticArrayInterface → StaticArrayInterfaceOffsetArraysExt
224.1 ms LoopVectorization
0.3 ms LoopVectorization → SpecialFunctionsExt
5.3 ms LoopVectorization → ForwardDiffExt
1.4 ms TriangularSolve
235.5 ms RecursiveFactorization
15.2 ms IterativeSolvers
34.5 ms KLU
3.7 ms Sparspak
6.7 ms FastLapackInterface
22.4 ms Krylov
52.5 ms KrylovKit
270.0 ms LinearSolve
696.5 ms StaticArrays
5.7 ms StaticArrayInterface → StaticArrayInterfaceStaticArraysExt
0.2 ms Adapt → AdaptStaticArraysExt
2.4 ms ConstructionBase → ConstructionBaseStaticArraysExt
0.7 ms ForwardDiff → ForwardDiffStaticArraysExt
5.8 ms FiniteDiff
104.8 ms SimpleNonlinearSolve
8.2 ms NLSolversBase
7.3 ms LineSearches
0.2 ms SimpleUnPack
93.8 ms DataStructures
38.0 ms GenericSchur
1544.0 ms ExponentialUtilities
3.1 ms SimpleTraits
4.4 ms ArnoldiMethod
1.0 ms Inflate
41.2 ms Graphs
0.6 ms VertexSafeGraphs
6.1 ms SparseDiffTools
255.3 ms NonlinearSolve
0.5 ms StatsAPI
5.8 ms Distances
2.9 ms NLsolve
0.9 ms SciMLNLSolve
1755.4 ms OrdinaryDiffEq
83.9 ms IntervalSets
0.8 ms ConstructionBase → ConstructionBaseIntervalSetsExt
2.0 ms CompositeTypes
224.1 ms DomainSets
0.5 ms Unityper
39.1 ms AbstractTrees
46.9 ms TimerOutputs
5.4 ms Combinatorics
565.9 ms MutableArithmetics
127.1 ms MultivariatePolynomials
35.1 ms DynamicPolynomials
2.0 ms Bijections
62.7 ms LabelledArrays
423.9 ms SymbolicUtils
0.4 ms TreeViews
41.3 ms RandomExtensions
12.7 ms GroupsCore
203.0 ms AbstractAlgebra
0.4 ms IntegerMathUtils
23.0 ms Primes
849.3 ms Groebner
0.7 ms SortingAlgorithms
20.8 ms Missings
31.8 ms StatsBase
48.6 ms PDMats
189.7 ms Rmath_jll 99.59% compilation time (100% recompilation)
1.1 ms Rmath
1.9 ms Calculus
33.3 ms DualNumbers
2.1 ms HypergeometricFunctions
5.5 ms StatsFuns
0.4 ms StatsFuns → StatsFunsChainRulesCoreExt
7.5 ms QuadGK
229.2 ms FillArrays
747.8 ms Distributions
1.2 ms Distributions → DistributionsChainRulesCoreExt
0.3 ms DiffEqBase → DiffEqBaseDistributionsExt
0.8 ms LaTeXStrings
1.1 ms Formatting
90.7 ms Latexify
10.1 ms LambertW
480.4 ms Symbolics
12.270529 seconds (12.59 M allocations: 775.836 MiB, 5.17% gc time, 3.68% compilation time: 42% of which was recompilation)
Here is the sorted list of the top 10 packages that take more than 300 ms to load.
1789.4 ms OrdinaryDiffEq
1578.9 ms ExponentialUtilities
872.6 ms Groebner
756.7 ms Distributions
687.8 ms StaticArrays
563.7 ms MutableArithmetics
485.4 ms Symbolics
427.1 ms SymbolicUtils
424.3 ms StrideArraysCore
312.6 ms VectorizationBase
These 10 packages account for 7.1 seconds out of the 12.2 seconds (58%) of the loading time.
You might want to take a look under your ~/.julia/compiled/v1.9 directory to see how large the shared libraries are for the respective packages (.so, .dll, .dylib). Scanning my .julia/compiled/v1.9 directory for those ten packages, I get the following.
$ du -hcs OrdinaryDiffEq ExponentialUtilities Groebner Distributions StaticArrays MutableArithmetics Symbolics SymbolicUtils StrideArraysCore VectorizationBase
151M OrdinaryDiffEq
16M ExponentialUtilities
11M Groebner
16M Distributions
75M StaticArrays
5.7M MutableArithmetics
14M Symbolics
15M SymbolicUtils
600K StrideArraysCore
19M VectorizationBase
320M total
As for your other idea of modifying the precompilation of your dependencies, you could also fork those packages, modify their top-level precompilation statements, and then provide your collaborators a Manifest.toml pointing at your forks.