05 corolla surpentine belt making noise at cold start

Hi I was wondering because surpentine belt is a big thing for 05 corolla since everything runs on it. I also had a 94 camry which had a alternator connected to a belt. and if i wanted to tigthen up that belt i would just loosen the alternator and pull it. Is there a way to tighten up supentine belt in my 05 corolla in the same way?. I would like to get a new belt but running short on money. please advice an alternative

Find out which pulley is making the noise and potentially has a bad bearing. Replace the accessory with the bad bearing.

You can test the tensioner and see if it is within spec. Then replace it if it is not in spec.

No way to adjust the belt tension.