I don't think your issue is not being able to wrap your mind around eternity and infinity. Your issue is that you somehow believed you were capable of doing such a thing in the FIRST place. Other people don't have faith in God because they can wrap their minds around those things. They believe in God and eternity and infinity IN SPITE of their lack of understanding of those things. The human mind CAN'T comprehend the incomprehensible. It never could, and anyone who tells you otherwise is just blowing smoke.
God has given humans the capacity to know that something exists, even if we can't know HOW that thing exists. For example, I can know that there is such a thing as timelessness (eternity), and yet, as a creature of time, I also understand that there is NOTHING in my life experience that I can point to that displays the characteristics of eternity. In fact, EVERYTHING around me is just as much a prisoner of time as I am. So, how do I know that there IS such a thing as eternity? Simply because God communicates it to me in His Word. I accept it on faith. Ecclesiastes 3:11 says, "...he has put eternity into man’s heart..." It's in our hearts, but NOT in our minds to comprehend it. We must leave room for that as a mystery of God.
Were I to say that eternity cannot exist simply because I cannot comprehend such a thing, I would essentially be declaring my mind to be the greatest thing in the Universe, and anything outside my mind (or beyond my mind) cannot possibly exist and is therefore untrue. That would be the height of human arrogance.
Many people over the years have confessed to me their inability to accept that God is a Trinity — one God and three Persons — because they cannot fathom how such a thing could be. But what they fail to realize is that if they COULD fathom the nature of God, their mind would be EQUAL to God. But, by definition, God MUST be greater than man, otherwise He would not be God. And if God is greater than man, then it is logical to believe that His nature is also greater than man's comprehension (or ability to know).
Now, the EXISTENCE of God is somewhat easier to establish, because unlike eternity, God has left His fingerprints on everything that I can see in my daily experience. The Apostle Paul explains that God's "...invisible attributes, namely, his eternal power and divine nature, have been clearly perceived, ever since the creation of the world, in the things that have been made." (Romans 1:20) The reason they are "clearly perceived" is because God has also given all of humankind the ability to recognize that which is the by-product of a designer versus that which is the by-product of random forces. For example, if an earthquake were to knock our Scrabble board game off the shelf and onto the floor, I would look at the arrangement of the letters and I would KNOW that the game ended up on the floor as a result of a random event. The very way they were sprawled on the floor would tell me that. If, however, I found that all the letters from the Scrabble game on the floor were arranged in such a way as to spell out a specific message to me with each word spelled correctly, I would know that someone (a designer) had arranged them that way. Why? Because random events of disorder never result in order and intelligence.
You have convinced yourself that your inability to fathom the incomprehensible is actually a "doubt" as to the existence of God. It is not. It is simply the result of your being a finite human being who CANNOT comprehend what is incomprehensible. The God who created all things and Who is yet uncreated has expressed it in His Word to us, when He says: "For my thoughts are not your thoughts, neither are your ways my ways, declares the LORD. For as the heavens are higher than the earth, so are my ways higher than your ways and my thoughts than your thoughts." (Isaiah 55:8–9)
The Apostle Paul expressed it this way: "Oh, the depth of the riches and wisdom and knowledge of God! How unsearchable are his judgments and how inscrutable* his ways! (Romans 11:33)
*impossible to understand or interpret.