From the Fifth Way to Omniscience?

Is it possible to infer from the workings of the universe the omniscience of God?

Thomas Aquinas argues in his Fifth Way that it is impossible to explain the determinations (teleology) exhibited by natural things without appeal to intellect.  My question is – can we go beyond that?  Can we, through examination of observable phenomena, reasonably infer the necessity of an omniscient being?

If we can infer intelligence from the behavior of mindless nature (as Aquinas argues), can we then look at the complexities of nature as a whole and – from that – infer omniscience?

It seems like it should be possible.  If you look at nature, there’s a lot going on.  Pretty much everything is busy doing something that fits into the giant puzzle somehow.  If you take all of it into account – every relation, of every thing, in every system, one to another – and consider the fact that the intelligence required by the Fifth Way would have to know and understand all of it, I sincerely think the case could be made.