I know that everyone here have an array of belief levels and how they perceive things. So I wanted to know, based on your methods of reasoning, can you prove that love exist? How would you access it, if you would at all?
English is at a huge disadvantage on this topic because, by itself, it has no way to distinguish between the various forms of love. There is the love found in romance, the love found within families, the love between friends and the love commonly referred to as Agape which Jesus is believed to reference in His teachings.
I suspect your question refers to Agape love. That is a love which is largely, if not completely, expressed by one's behavior. It is a love of humanity which is expressed by the way an individual treats everyone regardless of their status in life, race, sex, sexual expression, or any of the hundreds of ways we use as we create 'us' and 'them' pairings.
And since it is based on behavior..."Do unto others as you would have them do unto you"...proof of its existence should be obvious by simply watching how others behave. Those people who divide others into favored and unfavored groups don't have it. Those who are constantly reaching back to lift anyone and everyone up and puts those people ahead of them do have it.
IMMHO, expressing Agape love is the very core of being a Follower of Jesus. A Follower's behavior constantly shows the use of Agape love. Those who are do not show that behavior are not a Follower despite any and all assertions otherwise.
That is my opinion. The way Jesus put it was like this:
John 14:23-24
"Jesus replied, “Anyone who loves me will obey my teaching. My Father will love them, and we will come to them and make our home with them. 24 Anyone who does not love me will not obey my teaching. These words you hear are not my own; they belong to the Father who sent me."
The proof is the behavior of an individual as they interact with everyone on the planet, either as individuals or en-mass. We see the proof every time someone holds the door open for a stranger, when someone stops to aid a stranger, or when someone tries to stop a government from separating families over border issues.
There are as many examples as there are interactions between human beings. Every interaction provides the opportunity to express Agape love or reject it.