Krsna is the Supreme Personality of Godhead. How is that? Because He conforms in exact detail to descriptions of the Supreme Being, the Godhead. In other words, Krsna is the Godhead because He is all-attractive. Outside the principle of all-attraction, there is no meaning to the word “Godhead.” How is it one can be all-attractive? First of all, if one is very wealthy, if he has great riches, he becomes attractive to the people in general. Similarly, if someone is very powerful, he also becomes attractive, and if someone is very famous, he also becomes attractive, and if someone is very beautiful or wise or unattached to all kinds of possessions, he also becomes attractive. So from practical experience we can observe that one is attractive due to (1) wealth, (2) power, (3) fame, (4) beauty, (5) wisdom and (6) renunciation. One who is in possession of all six of these opulences at the same time, who possesses them to an unlimited degree, is understood to be the Supreme Personality of Godhead. These opulences of the Godhead are delineated by Parasara Muni, a great Vedic authority.
From Srila Prabhupada’s preface to “Krsna” book.
Once Srila Prabhupada asked his disciples (I believe this was room conversation in Bombay) this same question. Who is God? So, naturally everyone said Krishna is God. So he asked them if they were sure and how… One of them said "Prabhupad, Krishna says it Himself in BG" and he asked why i should believe BG? Another one said "All the acharyaa say so". Don't remember his response but he refuted this conclusion also. Then a third disciple said humbly, "Srila Prabhupad, as we do devotional service, we feel His presence, His energy etc…". Prabhupad liked this answer and said yes, we feel and that's how we can become convinced that Krishna is God. Lord Krishna confirms this in the 9th chapter of BG and as devotees we have many such experiences in our lives when we do devotional service or even try to…
Krishna reciprocates if we are sincere and there's no greater munificent acharya than our Srila Prabhupad. This I have experienced personally in my life. Many things I simply don't deserve but because I distributed a few of his books, he has petioned Krishna to bestow mercy on me…