To be clear we are — in the service of speed — trying to bake data into compiled program output binaries, which is ostensibly faster because code-pages in memory when executed by CPU as instructions already have it?
If all you want to do is bake data into a compiled program, there is the #embed feature added to C++26.
New (and delete) can be used in constexpr functions, however memory "allocated" like that cannot leave the constexpr "sandbox" so to speak, therefore std::vector cannot be generated at compile-time, but std::array may.
If you are working with fixed-size data like LUTs, just use std::array [1]
[1] Make sure not to use std::to_array when embedding 200KB+ files, as it's a mere constexpr function and not a language construct and will exceed constexpr limits; either specify the size or use a C-style array in this case