I don't think there's any magic trick or gadget that will help. Starting further down and backtacking is the answer for straight stitch, like you've been doing.

For the decorative stitch, try using a small piece of folded scrap fabric, instead of paper, 100% cotton if possible, and put that in the front to get a running start. You can leave a little break between that and what you're sewing so you can cut it off the scrap off, leaving a little bit of thread. Then that little bit of thread can be folded under and tacked down with a dot of fabric glue to keep it from unraveling.

Make sure you have the bobbin thread pulled up, and as you start sewing gently pull both the bobbin and upper threads toward the rear to keep them from getting pulled under and tangling

Start sewing with the feed dogs (those jagged teeth) at the machine cycle where they are as far forward as possible so they will move the fabric properly.

Sorry if this is too late but...

I always lower the needle into the fabric before starting - that's what I was taught. Also, the type & dullness of a needle can cause this. I see no mention of that above. Did you make sure you're using the appropriate type for your fabric? & also how old or new is the needle? I was taught to run my finger over the needle to check for burrs.