You start with 5000 bc in the bank, so losing money at the beginning of the game isn't a big problem. Just make sure you've built a profitable economy before the starting money is all gone.
Here's how the economy works. Your primary income early on is taxes. So grow your population, so that there are more taxpayers, and increase your tax rate to get more money. The catch is that a high tax rate reduces morale, which reduces your population growth. This is what I do: at the beginning of the game, set taxes low enough so that all your planets have 100% morale because this doubles your population growth. You'll be losing money, so when the starting 5000 bc is gone, increase taxes until morale on all your planets is just above 40%. You'll be making more money now, and your population will be growing at the normal rate as long as you keep morale above 40%. Also, build economic buildings on planets with high populations, and set up trade routes with distant planets for more income.
Planet maintenance, production, and research cost money, so you can save yourself from bankruptcy by reducing your spend rate, or by building fewer factories and labs.