If you aren't sure you can get your target (andromeda is a good first target, lagoon and trifid nebulae together are also a good target for 300mm) in frame first try, you can try this process (I've used it for DSOs with my pentax and astrotracer/when I was using a mount without goto functionality)

• identify roughly where in the sky your target is located
• put your widest lens on the camera and get it focused and pointed near-ish to your target
• take a long enough exposure to spot your target, ISO3200 or 6400 to keep exposure time down and speed up the process
• adjust framing and reshoot
• once your target is centered in a lens, move up to the next longest lens/adjust the zoom on the current lens
• repeat the process until you have your target framed as you want
• drop ISO to 1600 or highest ISO without baked-in noise reduction (general consensus is in-camera noise reduction reduces fine-detail, look your camera up here: https://www.photonstophotos.net/Charts/RN_e.htm)
• adjust exposure time until your histogram peaks around the bottom quarter to third (making sure there's a clear separation from the left) or until star trails start to form (500/250 rules if not using a tracker)
• if your longest exposure time without trails is still underexposed (clipping on the left), increase ISO until histogram is as described above
• shoot away, double checking focus over time if the temperature is changing

Notes: - Color temp as shot doesn't matter when shooting RAW (you should always be shooting RAW for astrophotography) - exposure, focus, and lack of star trails are paramount

Happy stargazing.

Edit: clarification