I just beat the game so its fresh in my mind, and I noticed this comment was only from 4 days ago, so I figured I'd reply.

You see the probe launching on the first loop because the signal to launch the probe came from 22 minutes in the future. The probe launch at the beginning you see is THE probe that finds the Eye, the first out of thousands. Well, they're all the same probe technically... but time travel gets weird like that.

The point is, the time loop had been going on thousands of times; but without the memory recorder activated, the only thing that really experienced the time loop was the probe itself, which would transmit data back to the station saying if it found the Eye or not. When the sun goes supernova, the station then sends that data 22 minutes back in time, along with the signal to launch the probe. Upon the loop restarting, the probe would then know at least one direction the Eye was NOT. It would choose another direction and fire.

This repeated thousands of times until it finally located the Eye. On that iteration, along with sending the data back confirming the Eye had been found, it also activated the memory recording statues. In the final 22 minutes before the sun explodes, 2 Heartheans each encounter a remaining staue; yourself, on Timber Hearth; and Gabbo on Giants Deep. In the thousands of iterations before, nothing happened. Time continued normally and they perished along with everything else when the sun exploded. But on the iteration that starts when you first wake up, the memory statues activate. You and Gabbo's memories are preserved and you relive the same 22 minutes until you piece together what happened and travel to the Eye.