When we flew into Burbank (Never, Ever Again!) in March we took a stroller and we deplaned onto the tarmac. We had to wait a few minutes for them to unload the stroller from the special stroller area. I expected it to be faster, but the plane wasn't very big and it didn't take very long to get off! We also had gate checked a high back booster seat and we got it at the same time as the stroller.
I would think that LGB would be about the same. It may take a minute or two for your stroller to be ready.

But it should be right there at the bottom of the stairs.