Here is your problem. If database A is suddenly corrupted, you will probably no longer be able to run it. Therefore, there would potentially be no viable infrastructure in which one could place a viable button such as you describe.
The file-picker dialog to browse a given folder and let you pick A-2018-07-01 or A-2018-07-08 or whatever other file you pick isn't the problem. It is where you could put this button such that it would still work that is the problem. Typically, corrupted databases stop working. Once that happens, NO buttons work.
Is this a shared or single-user database? If it is shared, I am also guessing here, but your question SOUNDS like you want your users to be able to do this. I believe this would be incredibly dangerous since in that case, it is the sort of thing that requires coordination among all users so that the "left hand knows what the right hand is doing." If TWO users attempted this at the same time and picked different backups to restore a shared database, chaos would follow closely.
Then, there is the question of whether this is a unified or split database. A split database has all data in a back-end (BE) file and everything else (queries, forms, reports, macros, modules) in a front-end (FE) file. A unified file is a single file that contains everything.
If the database is unified, you are dead in the water with having the database restore itself. It's like the old Warner Brothers cartoons where the character saws off the branch on where he is sitting and the rest of the tree falls down. You are in essence trying to replace the program you are actively using WHILE IT IS RUNNING. It is almost like you might imagine if a heart surgeon tried to transplant his own heart.
If the database is split, this potential update of the BE file (only) could occur, but only if you ALWAYS used late-linking on the FE so that it would come up "clean" and THEN be able to link to a given BE. No offense is intended, but given your description and the difficulty of setting up this kind of situation, I'm betting that you did not have this kind of set up. It would be beyond the skills of most beginners and even some mid-level developers.
Therefore, if you have a corrupted database, your better choice is to use WINDOWS (not Access) to just select and copy the file. Read through my answer to consider the factors. If you have further questions, please don't hesitate to ask.