While knowing what the seeds look like, it's just as important to know what the plant looks like and where it grows. This is what the plant looks like

DSCN1200 by Stuart Black, on Flickr

And this is what a patch of them can look like

DSCN1199 by Stuart Black, on Flickr

An individual tribulus terrestris plant spreads very wide and seldom grows more that 3/4" off the ground. It has small green leaves and yellow flowers. Each flower results in 5 seed pods and there can be thousands of flowers per plant. Wikipedia says that they can grow up to 6' in diameter but I've seen them in southern Colorado that are at least 6' in radius. It grows well in disturbed soils but does not compete with other plants well. Once grasses or other plants move into the area, the tribulus terrestris dies out and the seeds will lay fallow. The seeds can lay fallow for up to 50 years and still germinate. Since we humans like to disturb soils so much, it's a match made in heaven. The following picture shows how poorly they compete with grasses. The large patch of goat heads is on the right side of the fence in a vehicle parking lot. There are no goathead plants growing in the grass.

DSCN1202 by Stuart Black, on Flickr

Given what you've said above, I think part of your problem is that you don't recognize the plant and ride over it. You might also be riding in disturbed areas like new bike paths. Be aware that nothing is perfect...including tubeless. I've been on rides with people who have flatted tubeless tires on goatheads. Slime isn't perfect. Liners aren't perfect. "Thorn proof" tubes aren't and are, perhaps, the most useless of all the solutions. I use liners to good effect but they can still flat. I've used Slime and didn't find it was any better.

Don't tempt the goat head god either. It is a capricious and vengeful god! On the ride where the tubeless flatted, I managed to do the ride without a single flat. There were 4 people on the ride and we had 27 flats between the 4 of us. One poor woman had 20, the guy with the tubeless had 6 and my wife had 1 (I forgot to put a liner back in one of her tires). I crowed about how wonderful my liners were. The next time I went to the same area, I stopped counting at 65 punctures...on one tire. The other one had a similar number. The moral of the story is to be humble before the god of goat heads.

Epilogue: The next time I went to the same area (it a regular ride I take people on, see Wandering in Purgatory below), I decided to not take chances. I got used tires that I was just going to throw away after the ride, I put in liners and Slime tubes. The wheels weighed a ton! I did the entire ride with my daughter (similarly equipped) and we had zero flats between us. We picked up zero goat heads. I fear what the goat head god has in store for me next time I go down there!