The first new life heart you get is when you go to the first temple and beat the boss. When the boss dies you get another heart.
You can get the 1/8 piece of hearts that you need to collect 8 of to make one heart but that won't be immediate but you SHOULD do that if you want more health.
If you are talking about that cave right after where the guy sells you oil and you are searching for Talo you really don't need that many hearts. Just remember to Z target and you should be fine.
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(wiichat is bloked at chool