I have a 2017 Cannondale Synapse Carbon Disc 105 with less than 10 hours of ride time on it. (I got it in March as unsold stock from last year) I noticed that after I had ridden for a little while, the rear wheel started squeaking obnoxiously as I rode, even while coasting. After a bit of troubleshooting (i.e. removing the caliper), I determined the rear disc brake was definitely the problem; it was presumably misaligned or something. However, when trying to reinstall the caliper after learning this, I noticed the pads seem too close together, to the point where I had trouble fitting them back around the rotor. Now that I've roughly gotten the rear caliper into position, it is constantly rubbing against the rotor however I align it, and the brake lever feels much tighter. Again, this is a new bike with new Shimano 105 parts and I haven't changed anything out. What happened? How do I recalibrate the brake so it works properly? (If it turns out I somehow ruined something, I still have a warranty tune-up at my dealer where I can get it sorted out)
As mentioned in comments you most likely applied the brake without the disc between the pads. The pistons advance and do not return all the way to their original position - this is how hydraulic brakes automatically adjust for pad wear.
The pistons can be pushed back in. Remove the pads then use a tire lever to push the pistons back in. Then replace the pads. You should be able to find numerous videos showing you how to do this on YouTube.
You should check your disc is not warped, and then reinstall the caliper unit. Again there are plenty of how-to videos explaining how to align the caliper. One way is to loosen the caliper bolts, apply the brake so that the pads grip the rotor them tighten the bolts, then release the brake.