How is it possible to have one-way only lossless compression?
The same thing can be done with image data. For something like jpeg you can keep the coefficients but store them in a more compact form.
For what it's worth JPEG XL claims that it's 'reversible', but I'm not sure if that means you get your original jpeg back, byte for byte, or you get an equivalent jpeg back.
I don't think getting the same JPEG is the goal here but getting a JPEG that decodes to the same image data.
But it might be more hassle than it's worth it to create the code and algorithms to do so.
Btw, if memory serves right, Google Photos deliberately gives you back the same pixels but not the same JPEG codestream bits under some circumstances. That's too make it harder to exploit vulnerabilities with carefully crafted files.