I think I short-changed myself. Is it too late?

I went in for a Job interview 2 weeks ago and when she asked for a salary range I told her $14 an hour was the lowest. After we continued to talk she mentioned another position they had coming open and we spoke about it and she asked if I would be interested. I told her yes. Just got the call yesterday that I got the job (the one mentioned in the interview, not the one I interview for). They offered me $16 an hour, which I accepted. Signed my offer letter yesterday. Now I have looked up the average pay at the company for the position I got and it $20 an hour... I feel like it's too late to say something now. Is this just a lesson learned? Or is there a way I can bring it up? My start date is June 17th.

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