Thank you for this very good question. In this Scripture, the word used for “offering” would refer to anything presented to God, as in presenting a gift. Recall that in Matthew 2:11, the three wise men presented gifts to the baby Jesus.  Another word is sometimes used in Scripture meaning to offer up, as in the Lord Jesus offering up Himself as a sacrifice for our sins, in the manner in which the high priests of old offered up sacrifices: “For such an high priest became us, who is holy, harmless, undefiled, separate from sinners, and made higher than the heavens; Who needed not daily, as those high priests, to offer up sacrifice, first for his own sins, and then for the people’s: for this He did once, when He offered up Himself.” (Hebrews 7:26-27). 

But now, let’s consider the use of this word in the story of Cornelius whose conversion is at the center of Acts 10. Cornelius was a centurion, a Roman officer commanding 100 soldiers, and he was posted in Caesarea as part of the Roman occupation of Israel. This man, we read, loved God, even though he was a Gentile. How this came to be, we are not told, but only that he was “A devout man, and one that feared God with all his house, which gave much alms to the people, and prayed to God always.” (Verse 2). Perhaps being posted among the people of Israel, he came to love them and also their God. We do not read that he was yet saved, for in the very next chapter of Acts, we find that He was told by the angel that visited him that Peter would come to him “Who shall tell thee words, whereby thou and all thy house shall be saved.” (Acts 11:14). Perhaps he was a proselyte or becoming one, in other words perhaps he hoped to join the Jewish faith. In any case, he did have a heart for God, and this was revealed in his acts of kindness towards the Jewish people, and his prayers, all of which had been noted by and were pleasing to God. These prayers and good works done for God’s people were received with much favor by God, much like the sacrifices of our lips which we see in Hebrews 13:15-16, “By him therefore let us offer the sacrifice of praise to God continually, that is, the fruit of our lips giving thanks to his name. But to do good and to communicate forget not: for with such sacrifices God is well pleased.” Again, we read in Romans 12:1, “I beseech you therefore, brethren, by the mercies of God, that ye present your bodies a living sacrifice, holy, acceptable unto God, which is your reasonable service”.

So, in response to your question, I do believe that the heart of Cornelius was set on seeking the Lord, and his prayers and kind works towards the Jews was seen by God as an offering or sacrifice which was pleasing to the Lord.

Furthermore, it was because of this heart for the Lord and for His people, I believe, that the Lord sent the Apostle Peter to Cornelius, Gentile that he was, with the Gospel of life, whereby he might be saved. I do believe that when a soul, anywhere on earth, seeks the Lord, that the Lord will reveal Himself to them, and will bring to that one the light they need in order to be saved. We read in Jeremiah 29: 13, “And ye shall seek Me, and find Me, when ye shall search for Me with all your heart.” Paul in Athens told the philosophers on Mars Hill: “That they should seek the Lord, if haply they might feel after Him, and find Him, though He be not far from every one of us…,” (Acts 17: 27).

Now, how about you, dear friend? Have you believed on the Lord Jesus Christ as your Savior?  We read in John 1:12, “But as many as received Him, to them gave He power to become the sons of God, even to them that believe on His name…”.  (430.4)  (SF)