My 2010 corolla ran very very very low on oil. I would hear a rattling sound on startup. After refilling with oil the rattling has subsided but still continues on a cold start or first startup for the day. Once engine is warm there is no noise on startup.....can this be fixed.
Depending on how low on oil its been and how hot the internal parts have become, hopefully you may have only have suffered perhaps some wear in a hydraulic valve lifter or two. And the motor is noisier until the oil fills the hydraulic lifters. The noise really needs investigating though as depending on how noisy it is and what is actually causing it would better determine if further action was needed.
We can try and take a guess to advise you here but at the end of the day if this noise is due to something more serious then just a noisy lifter etc earlier attention and repair is better than waiting for a possible internal failure to occur.
If you live in a cold environment and your car is equipped with California emissions you have a secondary air pump somewhere. It's basically a fan that pumps air into the exhaust in order to satisfy EPA emissions. They are normally mounted to a steel bracket with rubber bushings to keep them quite when they turn on. If you can locate the pump and wiggle it back and forth and you hear a metal to metal sound the rubber bushings may be spent.