1. Keep your units few and un-upgraded. That contributes to a low Military score, making the AI more likely to attack you. Once they do, you can purchase units or upgrade. For example, a common thing that I do is that I leave Machinery one turn from being completed (so I can keep making cheap Archers). And then whenever I need to, I can then quickly upgrade into Crossbowmen.
2. GS has really reworked warmongering with the Grievance system. In the early game, I have found that civs can easily hate you. In my first GS game, I did two early surprise wars (against Zulu and Mali). That generated 300 grievance, giving me a -30 malus with everyone else. Shortly after, all the other civs started denouncing me and later did a bunch of joint wars against me. Prior to GS, people wouldn't care because this is Ancient Era warmongering. Now, you get the diplomatic penalty straight off with the grievances.