I hear this from almost every student I work with. "Am I behind?" "Is it too late?" "Should I even bother starting now?"
The answer is almost always no, you're not too late. And the reason I can say that is because every serious applicant feels behind. If everyone feels behind, then the playing field is more level than you think.
I started getting serious about my own application around winter break of my senior year. I really put my foot on the gas in late January. I took my last exam in April. I submitted everything. I got into Stanford.
Was that ideal? No. Did it work? Yes. Would I recommend cutting it that close? Also no. The point is that this process is more compressed than people expect, and the ones who actually lock in and execute tend to be fine even if they start later than they planned.