Can you show residency in ID? If not, you might not be able to register the trailer there.

We need to define a few things.

Title. In most states this just proves ownership.

What specific issues are there with getting a CA title? I've bought cars out of state the had a notary in the purchasing state witness the sellers signature / provide a note stating the car was sold for X $ . I then take this to a notary in my state to complete the process.

Registration ( License plate ) this allows the vehicle to be used on public roads.

You can get a paper temporary transit plate in the sellers state. You really need to do this to avoid on the road issues given the title will be somewhat convoluted.

In any event, make sure the title is in your name and clear once this is all over otherwise there will be issues down the road.