How might I successfully solo gank at level 1 with Phantom Assassin?

You don't. PA doesn't offer much to a gank as a level one hero beyond a 1-second slow and autoattacks.

PA is an end game hero. She does not have many useful active spells compared to other heroes, which is why she is not a good ganker early game.

Nevertheless if you really wanna gank around with her, you can try picking Blink and Dagger up until level 6 and hope you have a nice assisting/stunning/disabling hero with you when you're ganking!

I agree with others in PA inability to gank consistently at level 1. However, if you really insist on doing it,

I suggest you bring 2 supports with you (1 stunner or slower at least), you should level up phantom strike first as dagger does not provide much at level 1.

Position yourself and the support really well, don't go and hide yourself with the support as this will lead to suspicion of enemy heroes. Instead, lane as natural as possible and ask your support to rotate from behind before executing the lock down spell.

Observe and judge enemy hero before ganking as this will play great roles in determining the results. For example, you might not want to gank level 1 weaver with shukuchi.