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In the movie Frozen we see that Anna & Kristoff fooling around Olaf about snowman's fate in summer. At the end of movie Princess Elsa provides Olaf with means to survive summer.

How did he survive all summers from the time he was made till he remet Anna?

Did he exist throughout the time from when he was conceived or he appeared in the plot after Elsa fleed arendelle?

The living Olaf is made by Elsa while she's fleeing from Arendelle to North mountain (I think during the song, not sure). He has nothing to do with the regular snowman Olaf they made as kids. So there weren't any summers to survive.

There were no summers before he met Anna.

Olaf is created when Elsa sings "Let it go" as shown in the picture below.

After Elsa runs away, Anna immediately starts looking for her. Besides being her sister and caring for her, Anna also sees how Elsa's magic has frozen Arendelle in summer and believes that they need her to bring it back. From that point in time to the act of true love and Elsa actually thawing all the ice and snow only a few days pass.