Question on Index Fragmentation and Index Rebuilds

I am currently sitting with an Azure managed SQL-server, with all my table indexes sitting at >99% fragmentation. For some reason this instance was set to use DTU's, it's on a 250 tier. These tables are being constantly written and read from, and nightly data deleted. Is there a way I can rebuild the indexes while things are running without the risk of any of the other queries timing out? Or do I need to schedule some down time and kill the connections so that I can rebuild the indexes? Do I perhaps need to scale this DB up for this temporarily to something like 500 DTU's? I would appreciate any advice on what would be a good or a correct way to handle this. (Yes there is no DBA, no-one was looking at after this DB, I happen to notice this and now sit with this problem :(... )