A high-lift jack might do the trick. Think about watering around the posts that you want to pull. Pulling t-posts out of rock-hard dry ground is tough without hydraulics.
One can also “lever” the post up a few initial inches if you can attach a (near horizontal) lever to it. I’ve done that a couple times with a 4 x 4 and a big C-clamp. (Or even baling wire wrapped around several times.) Assuming one can dead lift 100 lbs. plus the 4 x 4, an 8 ft. 4 x 4 clamped on, one ft. from the end, gives you ~700 lbs. of force... 6” from the end gives less lift distance, but 1500 lbs. of “lift”.
Assuming the ground is not soft (add a patio block?), you’re in business.