For MTC tickets, they are available 24/7 through automated fare stations. Mega Bus, Greyhound, Jefferson Lines (and other regional lines) tickets are available online.
There are multiple services at Union Depot. If you're referring to Amtrak, I believe they sell tickets same day. They have been more full lately, so its risky to wait that late.
I'm not sure, you can always call to get the exact business hours...
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