I just finished an immense, crippling, TA 2.02, Drath victory. I (almost accidentally) achieved an influence victory. Since I had about 160 colonies to a total of maybe 20 for the three surviving AI civs, I suppose I could have started a war and won any kind of victory I wanted. I was about 70 turns from ascension. The game was about 7 1/2 years long.
I felt like I was stuck in the middle of the pack until I initiated my first war between my opponents, In a matter of weeks I was the only civ not at war and I was making serious BC off their wars.
I took all the planets that I acquired from major civs by influence. I was never at war with any major civ. My only significant military action was when the Jagged Knife took 34 of my planets, about 1/3 of my empire. It took about 4 months to get them all back. They managed to build one ship during that time.
I never had any large ship and only 4 medium combat vessels. They were for carrying my fleet attack modules.