Ah I've been shot down plenty of times for my attitude towards hydrometers...
You can measure, or at least should do immediately prior to pitching the yeast. One could argue that delay in pitching the yeast invites infection.
Then measure when you think fermentation has concluded, then again to make sure, then again to make doubly sure things haven't kicked off again...
Brewing commercial beer may be an exact science, I don't believe brewing beer at home is.
I don't use a hydrometer and indeed, have not, although I still have one in my kit box, for several years (I'm almost too embarrassed to state categorically exactly how many years...).
I'll just stand by for the flaming again, but I only do what works or me. If it doesn't work for others each to their own I say. Just be aware of the different methods available. I also don't use glad wrap for a lid for my fermenters...but then I've recently binned glass fermenter whilst working with my brain switched off...some might say that situation occurs more than I'd like to admit...
For the record I'm sipping quietly on a Pilsener to die for, brewed without the use of a hydrometer AND half of which was lost to mother earth after leaving the fermenter tap open...goes to show even the best beer can come from the worst experiences!