Sounds like too much weight forward. Flipping the stem is a good, no-cost option. Stretching and exercises to increase your abdominal strength front and back will also help. If flipping the stem doesn't help right away, get a shorter stem or one with more elevation. Then, as your core strength gets better, swap the old stem back in if you like.

Ideally, you should be able to remove your hands from the handlebars and still be able to hold yourself up.