Police can always arrest and detain you if they believe you committed a crime. There is a limit on how long they can hold you this way without an arrest warrant from a judge, though. They have to arraign you as soon as possible in that scenario. Which is why you really don't want to get picked up on a Friday because you coukd end up sitting in a holding cell until Monday and if the holding cells fill up they can book you into jail until your arraignment. Then, even if they take you to court Monday morning, you might sit there all day only for them to never make it to your docket and send you back to where they were holding you until the next day.

People with money and good lawyers will get their docket bumped up the line or even work deals with a judge after hours to get you released on bail or on your own recognizance until your arraignment.

A judge can issue an arrest warrant on their own, but when a grand jury is convened and issues an indictment, the judge presiding over the grand jury will ALWAYS issue an arrest warrant.

I am not a lawyer. This is all information I've picked up from watching police procedurals, true crime and forensic shows/documentaries, and reading about the prison industrial complex.