Well, one by-the-book answer is: don't.
The Daily Scrum is a 15-minute time-boxed event for the Development Team.
Your attendance is not required. And as long as you do your job in
Ensuring the Development Team understands items in the Product Backlog to the level needed.
There should be no problem.
Now the real world answer is probably more complex. My first question is, do you actually do Scrum, or do you manage a team in that stand-ups? Do you speak up without being asked a question? If so, you should check whether you really do Scrum.
Apart from time-travel, there are really only three choices:
- Find a time. We cannot do that for you. You have to do that with your team. There is no perfect solution.
- Find a person that is local to the team that can be a substitute for you. Might be a good idea anyway, since you might be out for a few days when you take days off or have to call in sick.
- Move to India
Nobody said working globally was easy... most companies do it because it's cheap, but they never calculate the real cost. Right now, you are shouldering that cost by yourself, hidden in your discomfort to be up super early or super late. They have outsourced labor to India and you pay parts of the cost that was "saved". If you don't like that, maybe a pay raise is in order, if you don't like it after that, maybe working with a company that employs local labor is better for your own health. The company bottom line is not your concern, your health and well-being is.