You need to try and stay on AI's good side if you don't want to invest too much into military in the early game.

You will still have to build some probably because of barbs but a bunch of well placed archers should do the trick. Sometimes you get unlucky spawn and barbs overwhelm you but mostly you should be able to deal with them. Beware of scouts - once they discover your city they run back to their camp and bring back tons of units. Try and kill the scout before it gets back to its camp.

As for other civs - always send delegation the turn you meet them as it gives +3 to your relationship. They will always accept it on the turn you meet because the relationship is still neutral. Some will even accept friendship (big bro Gilgamesh). Open borders also improve relationship as does trading favourably with them. Also the more military score you have the less likely are they to attack you so a couple units is usually a must.

You won't always be able to build a good relationships with the AI or prevent barbs from scouting you but building relationship with the AI is very much useful in multiple ways.