The attack is a kickdrum or has a kick drum layered onto it.
Try making the "hold" part of the bass - which is square and saw probably like you mentioned - and then add the first bit of a pretty high pitched kickdrum on top.
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I could achieve something similar by setting up a synth with some basic filter envelope (& distortion, eq blah you know the deal..) and applied heavy compression to it. Quick attack around 20 ms, release depending on the synth and melody you play with it. I layered a sub afterwards but both compressed together sounded good too.
The strong compression kicking in after a few ms gives you that thump effect and I believe it’s a better way than layering a kick sample, as the kick has to fit the synth material and sound good with all differently pitched notes (which it probably won’t).
