My original Exped Sleeping Mat had an awesome feature - its bag could be used to inflate the mat in seconds by attaching it to the mat's air intake and using it as a pump (see below for a more detailed explanation).
Unfortunately, that mat died - and its successor replaced the clever and light-weight bag/pump mechanism with a bulky and tediously slow 'built-in pump' system.
This thing attempts to resurrect the original mechanism by augmenting any large plastic bag + the top-end of a wide-mouth plastic bottle with a 3D-printed nozzle adapter. The result can inflate my sleeping mat in at most two 'puffs'. My next make will be tailored to my new inflatable kayak, meaning I can leave its pump at home too.
Use Customizer to tweak the parameters of your nozzle. Cut/drill a hole in the bottle cap to fit over your nozzle (to lock it into the bottle top-end). Use double-sided tape + regular tape to secure your nozzle+bottle-top-end into the corner of a large plastic bag - use lots of tape, as it needs to be strong and air-tight!
It is worth noting that Exped also appears to have resurrected this idea (as a separate product) - take a look at their page if my explanation above doesn't make sense (it's a bit hard to describe).