How do you manage trading on daily when close is at odd time?

I've seen that for people trading daily, they prefer candles that close at NY close time. My broker's daily candle also closes with NY close. And that time is 2 AM in my time zone which is a pretty odd time for me to be able to analyse chart since I have to be asleep at that time. I am wondering, how people manage trading daily when daily close is at odd times in your timezone?

When the daily candle close you have plenty of time to make a decision and take your trade. Till 4 am (your time) there is nothing serious happenning. At 4 am Sydney session opens. Due to its size, there is not much volatility. At 5 am Tokyo session opens. Again both together there is not much trading goes on(unless there is economical news of the important markets). What really matters is you to be at least ready on Europe opens (Frankfurt first then the FX giant London) by then you are up in the morning anyhow.

If you are trading on daily TF or even H4 it is not important what time the new bar opens. It is important that you have a trading plan. Because when the daily bar close you are not going to take position right away instead you will wait for a break or a specific zone,or price to be reached.

daily candle or trading long short close <24h ? I am a day trader but my candle is 15m 30m and 1h

Find another broker whose candles close at a different time?

Price doesn't move that much unless you are trading JPY pair. JPY also doesn't move everyday. The best option you research yourself and see what happens with price. And it's not necessary that you have to analyze just after the candle close. Yes in some days you may lose an opportunity but that's part of every business.