Hey again! Currently fixing the bug you mentioned, but I'm sorry - I'm a little confused what you mean in this comment!
It's true, you can't access saving/loading in the first 30 min of the game, and that is by design. You should be able to load your saves from the main menu, though, and I'm not quite getting where you're trying to load the game right now? That is unless you're playing in browser, which will be an issue - while the saves have been stored for some players, most seem to not be able to find/load saves. I'm really sorry if that's the case, since there isn't a way of restoring those saves if that is the case...
If the load menu doesn't show up on the main menu, it's because the game can't find any saves - it most likely means that either the saves have not been stored or they've been erased when playing in browser.
So sorry about your issues with the game, it sucks to lose progress like that and I wish there was an easy fix I could do. (The silver lining, I suppose, is that thanks to your report and the issues you've described, I'll be able to fix that bugs for tons of other players!)
Let me know if there's anything I can do to help!