car squells for a little while when you first start it. on 2003 Toyota Solara

eventually the squelling stops. And sometimes it starts back a little as you slow down and goes away as you speed up.

Asked by for the 2003 Toyota Solara
That sounds like a simple belt issue. im not familiar with that specific car but belt noise is extremely common. Take a look under your hood and feel your belts or have someone start it and watch it. look for a tensioner or even the alternator and just loosen it and use a pry bar or whatever will work to add more tension then just tighten the bolts. if its bad it should be obvious and in that case its the same scenario, loosen what needs to be loosened, pop the old belt off throw the new one on tension it up and tighten the bolts...done.