Can you actually fall in love in a month?

Anonymous
I'm 17 and I met an 18 year old guy at a summer group that lasted for 3 weeks in August, and I became good friends with him. In the 1st week, he had a crush on one girl as she was the first person at the group to properly talk to him. In the 2nd week, he liked a girl who was also a friend of mine, and was kind of with her. Then in the 3rd week he found out she was kissing her ex-boyfriend and was messing him around, so he realized she wasn't worth it. At the end of the 3rd week (late August) he told me he had started falling for me throughout the week.

I told him I only liked him as a friend, but I still gave it a chance. He did really sweet things eg wrote me poems, complimented me and called/texted me a lot. A couple of weeks later, he realized he liked me and the girl from the 2nd week at the same time, which caused us to fall out. About a week later we made up as friends. Another week after we made up (late September), he told me he had realized over the past few weeks and days that he was in love with me, and I gave him another chance, He's even said he loves me with all his heart, unconditionally, he knows I'm the one and has said he can't function properly in life without me.

I've wondered if he really could have loved me in a month and I've thought it may have been an infatuation. I asked him if he really knows it's love and not an infatuation, and he said he really does love me. Even though we're still involved and I've developed some feelings for him, my friends and sister all believe he doesn't actually love me. So, is it really possible for him to have fallen in love with me in a month, especially with the other girls he liked as well?
Can you actually fall in love in a month?
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