24 On the following day he entered Caesarea. Now Cornelius was waiting for them and had called together his relatives and close friends.
25 When Peter entered, Cornelius met him, and fell at his feet and worshiped him.
26 But Peter raised him up, saying, “Stand up; I too am just a man.”
Acts 10:24-26 (NASB)
There's no reason to believe Cornelius προσεκύνησεν Peter as 'God'.
First, regardless of the nuances of the word, there are plenty of examples of people performing this action to things which simply cannot be believed to be the God. Acts 7:43 discusses προσκυνεῖν to Moloch, and Matthew 4:9/Luke 4:7 have the devil asking Jesus to perform it to him.
Nor must it be to a god. In Revelation 13:4, the whole earth performs this act to the dragon and the beast. But perhaps more apt is Mt 18:26, where a slave who owes his anonymous lord money performs this act toward him. Especially looking at sources outside the NT, this act is performed toward anyone with authority significantly greater than that of the performer, and especially in times of duress (although the mere presence of a powerful-enough figure often caused duress). This is then captured in lexicons like LSJ which start with:
A.I.1 make obeisance to the gods or their images
...but then also include:
A.I.2 esp. of the Oriental fashion of prostrating oneself before kings and superiors
A.2.1 later, kiss
Hence, when John tries to προσκυνῆσαι to the angel in Rev 19 and 22, the answer "don't do that; I am a fellow slave; do it to God" is an attempt to put them on an even footing, so that προσκύνησις is not appropriate, rather than an attempt to say "only God is worthy of προσκύνησις". Peter's reaction in Acts 10 is similar.
Second, the word itself has a meaning, but our English word "worship" has strayed from it quite a bit, as did the Latin "adore" before it, as did the Greek before it.
The oldest meaning was to lower oneself physically to symbolize the cultural debasing before someone of higher authority. We don't know from the word itself whether this was anywhere from lying down flat to kneeling to bowing to inclining the head, although some verses cut out the latter options when they say the person "fell at his feet and...". As Liddell-Scott pointed out above, the later term was "kiss"*; their sources for that meaning begin around the 2nd century BC. It is significant that the (even later) word προσκυνητήριον is listed as a "stool for kneeling at prayer", not a "stool for kissing". This semantic development from a very physical act to an easier act to eventually a symbol of the act is no surprise to any student of linguistic abstraction.
The Latin Vulgate then translated "προσκυνέω" as "adoro", for example in Matthew 4:
et dixit illi haec tibi omnia dabo si cadens adoraveris me
...which doesn't come from a root meaning "to kneel" or "to kiss" but "to speak/ask/beg" and then "to admire". Which again is no surprise, being another natural abstraction stage.
Finally, the King James (etc) translated that as "worship", which, for example, as early as 1828 still meant "adore", and in the noun form "worthy" (although even in 1828 "in this sense, the word is nearly or quite obsolete"). But today it is defined as "to show respect and love for God or for a god especially by praying, having religious services, etc." In many churches I've been in, it means "sing songs to God" almost exclusively. Again, the natural development has been from harder physical acts to easier physical acts to ideas and feelings.
Therefore, it's a bit of an anachronism to read the English word "worship" backwards to the text to always mean "declare God as worthy" (or worse, "feel love toward God" or "sing").