This pattern is used to say that even if you do a certain action, it's useless or won't lead to a solution. It often appears in spoken Japanese when someone is worrying, complaining, or making excuses. The nuance is that you should stop doing that and accept reality or take a more effective action.

It attaches to the て-form of verbs or adjectives. For example, 考えて is the て-form of 考える, so 考えても始まらない means 'even if I think about it, it's no use.' Similarly, 文句を言って is the て-form of 文句を言う, so 文句を言っても始まらない means 'complaining is pointless.'

This expression is fairly common in everyday conversation, though it sounds a bit blunt. It's not rude, but it's direct. You can use it with friends or colleagues, but be careful not to sound dismissive.

Note that the verb 始まる usually means 'to begin,' but here it means 'to be meaningful' or 'to have a point.' So the literal idea is 'even if you do X, it won't get started,' meaning it won't lead anywhere.