Tridents are certainly fecund. Trees here always produce a load of seed and we end up with thousands of seedlings in the garden beds every spring.
Seed ripens in fall. Seed tends to hang on the trees even after the leaves drop and the large bunches make it very easy to pick.
Take a look around the parking area to see if you can spot seedlings. Seeds can blow some distance on the wind and grow very easily so there's likely to be some seedlings growing in nearby garden beds, cracks in pavement, behind buildings, etc depending how diligent the maintenance guys are. This year's seedlings will only be a few inches tall by now but there may be some older ones growing through those adjacent bushes.
Pulling seedlings saves the hassle of germinating seeds and will put you a year ahead anyway.