You could add a deps/build.jl to your package:
https://pkgdocs.julialang.org/v1/creating-packages/#Adding-a-build-step-to-the-package
More packages used to do this, but this created a rather terrible user experience. Most now use BinaryBuilder via Yggdrasil because this works quite reliably and does not impose many requirements upon the user. This will produce a JLL package.
If the user really wanted to build the binaries on their machine, they can use the JLL override mechanism via a Override.toml in the Julia depot or a LocalPreferences.toml with the Julia project.
https://docs.binarybuilder.org/stable/jll/#Overriding-specific-products