This is a really common problem, easily solved. I'm wondering, though, before you try the methods above, if your stitches are going smoothly otherwise? Take a scrap and try starting your stitching about a inch from the end. Start with needle down, then make sure the presser foot is down, then sew. Everything smooth this way or is the thread flying out of the needle hole? are you getting any birds' nests under the fabric ? any foul sound (other than maybe bad words --LOL). If there's any of that, then rethread the machine, change tension little by little, till the stitches in are looking good.
Some needles just need to "take a bite" out of fabric when they start, and sometimes the bite isn't big enough, so it lands in the feed dogs. Using "leader" or scrap ahead of the "good" fabric you're sewing , will let your needle take that bite.