Shifting from culture to SR

I've been playing cultural games for a couple of months, but i felt like it is time to turn towards a space race on emperor difficulty. To be honest I don't have too much experience with space races in general. So I just made a number of unsuccessful tries...

What I did was launching a praetorian rush on one or two AI to get about 7-10 cities and beeling for Liberalism to get the techs needed as fast as possible, only to be beat by the AI just a few rounds before the ship is ready. I usually made a solid overall game but I couldn't get away victorious.

Now I wonder if there is a way to get a sufficient number of cities without warmongering and aim at the space race right from the beginning.
Maybe you can help me out.

Thank you in advance

I rexed to 14 cities in a Huge / Epic / Spacerace I played lately. I still conquered up to 40 cities with Rifles, but I could have won from 14 cities without a problem.

Which level are you playing, and are you aware of the power of Corporations?

I play vanilla, I guess corporations are a concept from one the expansions.

Regarding REXing I always struggle to maintain my economy...

forgot to mention the level: Emperor

I unfortunately can only give feedback on BtS, as I've played exactly 1 vanilla-spacerace, and I remember them being very different on vanilla. Like Caste-system didn't have the extra , therefore worthless, building Wealth and Science has a 50% handicap, again, worthless...

If you got trouble to keep your economy, you must connect your cities between each other and with a foreign civ, either via roads or via rivers + sailing. Once you got Currency, every city can pay for itself if it's connected / has foreign Traderoutes.

The biggest difference between BTS and vanilla space victory is : in vanilla, you win when you launch your spaceship first.
In BTS, your spaceship has to arrive first at alpha centauri which will take extra turns.

In vanila, you can easily lanch in 1800 with ~30 cities... 15 cities should get you there by 1850, and even as few as 10 cities should allow you to launch before 1900, any of which should easily beat the AI.

This assumes that you can keep the peace, and are not required to build any defencive military. The biggest threat to winning the space race is an untimely declaration of war. So, as in many other play stiles, diplomacy is a major key.