Is it a way my girlfriend from the Philippines live in the US without marriage right away, she has visit here already

If you are a USC, and you inted to marry her within 90 days of her arrival, you can petition for her K1 visa. 

Your girlfriend would need a nonimmigrant visa that allows her to remain in the country for a longer period of time. She could look into applying for a student visa or work visa. This would allow her to remain in the country for a longer period of time without you having to rush to marry.