Need to go to rameshwaram from bangalore, do darshan and return same day, also want to do mani darshan which happens 5-6AM only

Hello people of bangalore, I want to go to rameshwaram. I am traveling alone and want to schedule something like - leave from bangalore at day0 evening , reach rameshwaram day1, then leave from rameshwaram day1 evening and be in bangalore day2 morning/afternoon. I read that there is mani darshan as well, which is open from 5AM to 6AM.I wanted to do that as well. I was checking for bus, as there are direct buses but all of them reach rameshwaram around 7AM.

Is there anyway I can reach there by around 4AM? I checked trains too but no direct train, and being alone I don't find it safe to change train mid night.A

P. S : All suggestions for first time solo traveller to rameshwaram are welcome. 🙂