Hello,
Congratulations! With your score you have chances of getting into top government medical college , of your state as usually cutoff is around was 550+ for UR category under 85% quota and good government colleges under 15% all india quota too.

With 604 NEET score your Overall Percentile will be around  98.18 - 99.78  and your NEET AIR Rank will be around 1979 - 2029

However it is difficult to predict AIIMS cutoff as it is the fisrt time AIIMS,JIPMER central institutions admissions will be through NEET scores.

However these information is based on last years cutoff and as cutoff changes every year depending on factors like difficulty and number of candidates and recent COVID19 situation etc.

You can use careers360 college predictor to know the colleges you can get at your NEET score;-

https://medicine.careers360.com/neet-college-predictor