This answer is for working in tech in the United Kingdom but may apply more generally.
References (usually two) are commonly required as part of, or after, the interview process, i.e. once you've cleared the first hurdle(s) of the job application process. Employers don't want to waste time checking references for people they might not want to make an offer to. However, when you are asked for references, you should have some contact information ready to give.
Depending on your workplace and how it is structured, and depending on the places you're applying to, you may be able to give references from coworkers who aren't your direct manager. It's common for e.g. a tech lead to be used as a reference even if they're not your line manager. I've also used more senior developers who I've worked closely with on my most recent project as references in the past.
The key is to find someone (or several someones) who you can trust to keep this information confidential and who can give a meaningful reference. Especially in the tech sector, a more senior person who you work with regularly will be able to give more meaningful references than someone who manages you but doesn't have daily contact with you.
In a pinch, you can also use past managers or coworkers, assuming you have a previous job that's not too far in the past. Generally I would say to have at least one reference from your current role if at all possible. However, hiring managers are people rather than robots and if you have a nonstandard set of references but a good reason for it, you can simply explain that. For example, if the job you're applying for involves mostly working with a specific technology, you can give references from a previous job where you worked more closely with that technology.