You own it the moment you press the shutter
Copyright in a photograph is automatic and belongs to the photographer (with some exceptions for work-for-hire). You don't need to register to own it.
When to register a photo
Register on Form VA at copyright.gov — you can register many photos in a single group submission, which photographers use to cover a whole shoot affordably. Registration is required to sue and to claim statutory damages, which matter a lot for images because actual damages per photo are often small.
Metadata helps, but it's not proof
EXIF data (camera, date, GPS) is useful but trivially edited or stripped when images are uploaded to social platforms. It is not reliable evidence of who shot a photo or when.
Timestamp your shots for tamper-proof proof
A blockchain timestamp creates evidence that can't be quietly altered. Hash your original RAW/JPEG with BlockchainSign — the fingerprint is computed in your browser, recorded on Ethereum, and returned as a lifetime certificate. If someone claims your image, you can show your original file existed on your shoot date. For volume, timestamp a ZIP of a shoot to cover many photos at once.