Humans used to hunt mammoths, and these fuckers don't even have a thick layer of fur armor. We used to hunt mammoths, because we were so fucking good at it we killed every last one of them.

I'm using my knife and making an atlatl, some spears smeared in shit, and I'm going hunting. Every time this bastard goes to sleep, he's getting a spear with a side of gangrene lodged in him. Fucker's missed out on 60 million years of techtree development, and has no reply to ranged strikes.

Guys I just checked t Rex extinct easy money they already ded

Do not leave the hut. Eat like an animal and throw your shit from the hut at the T-Rex's face. Hopefully it will get sick and perish on it's own from explosive T-Rex diarrhea.

T-Rex were believed to be fast for their size, but they couldn't take sharp turns.

That T-Rex is missing its feathers

Scenario didn't say you had to stay in the hut, or that you couldn't leave the the arena, or that others couldn't do the fighting for you with other weapons.

I'll just show up with a flu.

Wait can a T-Rex go an entire month without food? Are they feeding the thing while I am in there?

I would wait and hide, allowing the T-Rex to tire itself out. Then one night, when the T-Rex was especially tired and soundly asleep, I would carefully climb into the T-Rex’s cloaca. There I would stay for the rest of the month.

That’s it, you can keep the 500 million. I’ve already won.

I will craft a rudimentary instrument using any materials available in my hut and using my very high charisma I will seduce the beast.

I think some of the other suggestions are better, but my first thought was burying the knife in its food supply (assumings it's being given like entire dead cows or something) and hoping it takes a big enough bite to swallow it.

I imagine that blade going through the digestive track has a good chance to kill it.

Do I get to choose the food and can I use it towards the production of improvised weapons, including chemical and bio weapons? Can I stay in the hut and throw things outside the hut?

If yes, sure.

Alternatively: is the t-rex provided food during this time?

Keep feeding the t-rex with my unlimited supply of food. It will overeat and get lazy.

I've seen it happen with birds. If they eat too much you can just walk over and pick them up.

The T rex must sleep at some point. Find a big artery close to the skin surface, sever it. Watch it bleed out to death.

Or just stay in the hut and enjoy one month of free food and rent.