I agree with never giving them the 'free' cards - but that isn't the problem in the OP's question. Nothing 'free' about the chronic ATC players who bet anything and everything.
I'm more conservative than a lot of NL players (being an old time limit player), so I play early more on position and situation. If the lukbox lotto players are behind me, I always try to think if the hand I have is worth playing at all, knowing I will likely see another raise or an all-in. I will fold a decent hand if we are still in the donkfest stages, especially if it looks like it will be a multi-way pot.
The brave and daring will argue that it's all about taking risks, values, equities, odds
, percentages, etc. I argue that my decision is based in how much I value my MTT / tourney life. If you choose to be among the brave and daring, just be prepared to rebuy, reload, or run fast to all the site lobbies to see what is next on the agenda. If you place all your chips in the hands of Lady Luck, all I can say is 'GOOD luck', you'll need it.
There is only one way I know of to avoid these situations. It's called 'hitting the fold button'. No matter what you bet, raise, re-raise, re-re-raise, you will get called. These players get an adrenalin rush from someone 'pushing' them all in. It's what they live for.
Two things happen, IMO, in those early levels. The lucky ones get a big stack and the unlucky ones get their AA cracked and an all-out. Patience !! There WILL be hands worth playing where you whittle away at those donkey big-stacks. They'll be giving chips away shortly.