I bought an adaptor for Presta valves to fit into Schrader chucks. With that adaptor I can use the compressed air lines at service stations (ie those places where drivers refuel cars).
The compressed air lines are connected to rather large reservoirs, which allows large air flow.
However, at the place I've been to there's bit a lot of fine control. Just an on/off button. At first I remove the valve core and loosely put the chuck onto the empty valve stem. That way the air goes into the tyre as long as the bead isn't seated, and no pressure builds. As soon as the bead snapped into place, pressure builds and the chuck blows off.
Next I replace the valve core, connect adaptor and chuck, and carefully toggle the compressed air button. Using short bursts. By that time usually the bead is partly unseated already. But it seals enough for pressure to build despite the valve, and thus seat the bead again.
With the filled tyre I proceed home, and top up the air a couple of times over the next hours. All tubeless tyres I tried stayed in the rim or were easy to seat after being seated for a couple of hours. I'll deflate then, remove the valve core, fill in sealant, replace the core and inflate again.
By the time I bother with a service station, I've already spent a few hours of fruitless attempts at mounting the tyre with a track pump. To make that possible in the first place I do the following:
Leave the tyre inflated with an inner tube, for a fortnight or so.
Put a few drops of sealant at the valve stem and let it coagulate
Push the bead carefully against the rim's shoulders
Wet the bead with soapy water
In my experience, tricks with a length of webbing (ie those nylon bands used to secure cargo) spun around the circumference of the tyre do not work with supple narrow to medium tyres (<40 mm).
I repeatedly tried a barrage of expletives directed at the tyre. While it appeared to be exactly the right thing, it did not do any good. Threatening the tyre was hardly more useful. Nonetheless, I highly recommend doing both.