It’s normal. Most digital cameras and phones automatically embed thumbnails in the metadata of the photos they create. These are typically only a few kilobytes in size and can be extracted (along with the rest of the metadata) before the main part of the file is loaded. The thumbnail of the photo can therefore be displayed quite quickly, and the same goes for processing whatever other relevant information is included in the metadata.
This still leaves the rest of the file to be uploaded, though. The exact time this takes will of course depend mainly on the size of the original file and the capabilities of your internet connection. If you upload your photos in batches, the iNat uploader can improve matters somewhat by processing several at a once in parallel. But there’s really no way to avoid the overall cost: uploading large amounts of data via a standard internet connection is never going to be a quick operation.
The only real issue here is the “Loading metadata…” message that is shown whilst all of this is happening. It would be helpful if at some point the message changed to something like “Loading main file (5Mb) …”, so that it’s clearer what is actually causing the delay. This would also give a strong hint that it pays to crop all your photos before uploading them. Quite apart from the time this will save you, it is also a very community-friendly thing to do, since (amongst other things) it makes it clear what the subject of your photo is and improves the chances of it being identified.