Pre-Dominiom war when everything is pretty chill. Starfleet kinda seems fun until you realize that you have to basically do military training and all this bullshit to join and then you gotta go die in space half the time. I'd maybe just try and get a runabout or the equivalent and just sorta wander around with some pals and look at totally safe and previously explored space things. I would also open a Volcel Precinct on Risa.
Go through Starfleet Academy and work hard for years rising through the ranks...
... or walk into the Holodeck and pretend you're Indiana Jones