For all practicality space is infinite. We don’t know otherwise.
The concept that spacetime is expanding is kind of moot in relationship to your question, because it implies there’s an “end” to “out there” which there isn’t. We live in a cosmos with trillions of gallaxies and bazillions (fake work that gets the point accross) of stars with billions of bazillions of planets. Nobody can say they are in the center. Nobody says, oops, I just found the end.
It’s a mysterious concept spacetime and expansion. All we know is that it does appear to be expanding. We don’t know, and will probably never know for sure, how far it goes, if not infinite.