I just had my alternator replaced about 2 weeks ago by Cox. After the replacement I have been noticing my car is making a very strange noise at startup while the car is warming up. If the car is already warm and I start it up the noise doesn't happen. The car only makes the noise like the first 2 minutes while it's warming up. What could this possibly be? Could the mechanics have messed up on my car?

It's a Hyundai Tiburon '04

Thanks

You may be experiencing a form of repair-related anxiety.
Often, once a repair has been effected, the driver/operator will begin to notice things about their vehicle unrelated to the repair that was not noticed prior to being serviced.
This is not uncommon. Believe me.
If your car is operating the way you drove it prior, monitor the "noises" and keep track.
It may be just fine.

Sounds like a drive belt?

My mom's boyfriend is thinking it's the steering belt. He said they have to take it out when they replace the alternator and he said it could have gotten loose. Is that a possibility?

I'm going to the Hyundai dealership pretty soon when I have time because I just had all my belts changed about 2 months ago. So he was saying they should tighten everything up for free if that's the problem.

My mom's boyfriend is thinking its the steering belt. He said they have to take it out when they replace the alternator and he said it could have gotten loose. Is that a possibility?

I'm going to the Hyundai dealership pretty soon when i have time because i just had all my belts changed about 2 months ago. So he was saying they should tighten everything up for free if thats the problem.

Yes, that is definitely a possibility.
Adjusting new belts shortly after replacement is not uncommon. Whether they do it for free or a nominal charge will be the question.