Is there quick setting “gap filling” adhesive?
This can depend on the size of the gap and the materials being joined.  Two options come to mind that differ extremely.

First there is '5 minute' epoxy.  Mix the two parts, hold for approx five minutes and its pretty set.

Second, for very small gaps, there is gap filling Cyanoacrylate glue.  Then to get it to set  fast you can use an accelerator that you spray on to it once its where you want.  I doubt this is what you are looking for though.  Its common to use this approach for filling voids in wood before finish sanding.