LOTRO: Is it possible to get 3000 turbine points in F2P without buying them?

It will take a while but yes, it is possible to earn up to like 5500 TP with one toon. Remember, with the free to play account you can have 2 toons and EACH can earn TP that either can use. So, it is possible to earn up to like 11000 TP. Do your Deeds, those give 5 or 10 TPs each.