Why does the first Season of Naruto have different Openings at the same time?
Generally, when it comes to anime, OPs are switched out every season (12-13 episodes/weeks) or so. This is also the reason why 2-season anime series mostly have 2 different OPs, and single-season anime(s) only have 1 OP.

Since Naruto's 1st season has 35 episodes (according to Wikipedia), it makes sense that there are 3 different openings: the 1st season of Naruto is a roughly-3-season show, meaning that there will be 3 different openings.

If you meant "Why not forget about having different OPs in the first place?" as your question, it's hard to answer. It could be that production studios might want to inject some variety into the series, so that people don't get bored of watching the same opening 10, 20, or even 30 times.