I have really been enjoying this game; we play it a lot at work over lunch. I haven't kept track, but I'm pretty sure the victories are roughly evenly split. You are correct that in a game with fewer than 8 players, the first mission almost always goes to the Resistance because the Spies aren't willing to risk being found out. This isn't an issue with 8+ players, because the first mission is three people and it's not so dangerous for the spies to sabotage then.
A 7-player game isn't really that hard for the Resistance to win. As we've said, they can generally count on winning the 1st mission. They can also usually count on winning the 4th mission, since the Spies need two votes to fail that mission. So they only need to win one of the remaining three missions. The 5th mission is difficult to win, because the Resistance must correctly pick every Resistance member. However, the 2nd and 3rd missions are doable. Generally if it gets to the 5th mission, the Spies will win, unless the Resistance players have figured everyone out.
An important thing to remember is that you often gain more information from the team votes than from the mission votes. It's generally very telling when someone votes against a mission team. A simple strategy that often works well is to simply repeat successful (for the Resistance) teams. For example, if the Resistance wins the 2nd mission, simply repeat the same three people for the 3rd mission. It's possible there was a Spy in the group, but it's unlikely they would have let the Resistance get a 2nd victory so early (assuming they won the 1st). Anyone that votes against this repeat team is likely a Spy. If the leader refuses to repeat the same team, they are likely a Spy. You can use the same strategy with the 4th mission. If the Resistance won the 3rd mission, simply repeat the same three people plus one more. Since the Spies will need two fail votes, if the previous three were all Resistance they will win again. Obviously, the Spies will vote against this (unless there was a Spy in the previous group). So if the Resistance wins either the 2nd or 3rd mission, just make sure the same three people are on the next team. If the Resistance doesn't win either the 2nd or 3rd they are in trouble, because even if they win the 4th, the 5th will be tough.
Also, keep in mind that in the early part of the game only the Spies have a good reason to vote against a team. A Resistance player would only vote against the 1st team if they were playing a hunch or trying to get the leadership to move closer to them. Likewise, assuming the 1st mission goes to the Resistance and the same two people are proposed for the 2nd mission, only a Spy would generally have cause to vote against the team as the Resistance players don't have much to go on.