This always goes the same way.
You need to find yourself a used USA p-bass.
Scenario 1: You buy a squier pbass, but you wonder if you don't have a "real" Fender. You get a MIM fender, and then wonder if it would be better if you had a MIM or MIJ fender. With your new MIM or MIJ fender, you wonder if you are missing something not having a USA fender. You eventually get a USA fender. At Each stage of this scenario you ask for talkbass opinions and this does nothing to satisfy your curiosity, and only makes you more curious.
Scenario 1a: You are satisfied with the USA fender. Talkbass was leaning slightly to "fender is the best" that day. (now you start to question pick ups, strings, amps, pedals etc...)
Scenario 1b: Talkbass was leaning slightly to "fender is not the best" that day, so you search for a G&L, Lull, Nash, or some other P bass clone that is more expensive than your USA fender.
Either way, you've spent a ton of time and money instead of starting from a USA fender.
Scenario 2: You don't get a fender. You get a G&L tribute, a Lull, or any of the other pbass clones from every company out there. You always wonder if you should get a "real" fender pbass. You probably end up getting one a few years later and either tell talkbass that you wasted time with the other bass, or that fender isn't all that. Talkbass responds with 50% love or hate for your decision.
The only people who care what the headstock of your bass says is other musicians. With that said, i have about 3 US made fender precisions. I've seen guys with squiers that sound great, and guys with super fancy US made instruments sound bad.
Good luck!