How can I access Time Machine backups while my MacBook Pro repairs itself?

My MacBook crashed recently. I got the question mark, so I started internet recovery & had the OS saved to a USB. It had me log into my usual acct in the process, so I assume my stuff is still there. It finished the download & spent over 24hrs installing & restarting. So I took it to the Apple Store & they said to let it finish cuz it seems to be working through the repair just fine, just really slow. Now it's been a few more days & a cursor appeared, but it's still going. What are the odds it actually works in the end & what's the max amount of time it could take? I really need to access something on my TM asap, but I won't be able to get a new computer anytime soon. Is there any other way I can access TM temporarily?

[Re-Titled by Moderator]