[Qqqwxs]

GPS determines a solution for position and time simultaneously. It requires 4 satellites to solve for 4 unknowns (X, Y, Z, t). If you know your position you can solve for time using only 1 satellite, but a watch is always moving so it's position won't be known.

[defrost]

You might want to rethink that.

There's no need to 'solve' for time - it's included in the raw data packet from any single satellite.

As any 'solution' carries an inherent error margin, the desire for an excess of sats doesn't stem from solving for time but the reduction of error.

[Qqqwxs]

More specifically, you need to solve for the receiver clock bias.

https://www.e-education.psu.edu/geog862/node/1724

Edit: I would welcome corrections though if I am misunderstanding. Perhaps if you're not interested in precise timing you can read the satellite time from the broadcast signal?

Edit 2: OK, I think I understand your point now. The satellites broadcast their timestamps directly. To find a precise position / time you need to find a correction to the receiver clock. But if you don't need a very precise time, you can just use the satellite timestamp.