Almost all command line interfaces have man pages. Here's an excerpt from a copy of man epiphany-browser I found online:
SYNOPSIS
epiphany [OPTION...] [url]
--profile=FILE
Profile directory to use in the private instance
-a isn't in the copy I found, but it should be in yours (type man epiphany-browser at the command prompt); I'm guessing it's the short form of --application-mode. If that requires an argument, you should provide it.
If not, you should be fine by either getting rid of --profile, or providing an arg for that as well. You could also try -- (notice the spaces) before the URL; some CLI's respect this to indicate the end of arguments:
epiphany-browser -a --profile -- http://www.google.com
Of course, this is still an error since the --profile is pointless with no arg, but it may not be fatal and the URL may be recognized as such.