Trust me, emperor is not so bad, try deity, they run away very fast.
On deity you really have little choice but to conquer.
On Emperor you can do it peacefully with a few thing you must keep in mind.
1. You need to push lots of settler early. An absolute minimum cities would be 6.
2. You need to get most eurekas... look forward in the science tree for what you need
3. Get at least 2 campuses down early. For every tech you discover the cost of building a district goes up by about 8 production. The cost is worked out when you place them, not when you finish them
4 look toward you adjacency and double science district cards.
The most important thing as already mentioned is do not panic, it's natural to be behind unless you really push science hard, it's not the end of the world. Just make sure you have a fair sized Military.