The idea of “experiencing” reality is a contradiction in terms. The universe is not a movie watch. The spectrum of the waves we experience is very narrow. Electromagnetic waves alone include microwaves, gamma rays, X-rays, light (including ultraviolet, infrared...)... We don’t feel or see fields (magnetic, gravitational or otherwise), we hear a limited range of sounds... I could keep going.
On top of that, we never really experience any of those fenomena. We have receptors that capture waves of different nature and translate them into images, or sounds, or heat... Light is not there to be seen. It’s a phenomena, just like x-ray or microwaves. We revolved to capture a tiny spectrum of those waves and “think” we experience their existence or nature. Even the brightest star is not luminous. That’s your human perception. The whole universe is a dark gigantic interaction of energies and fields. Stars aren’t shining. En electron is not sparkling or firing, that’s all human perception. We think light is there to be seen, or sound is there to be heard, but it’s just the way our brain evolved and a trick to handle the capacity of some proteins to ineterct with phenomena. Math is similar to vision or hearing. It allows our brain to translate phenomena in something we can handle and usually understand. But math is not experience of the universe.
Think of the radio. A radio station somewhere is emitting radio waves (also electromagnetic waves) that travel near the speed of light (of course they are both very similar) there are all sorts of radio waves hitting your body at any given time, but you have no perception of them. They are just like the light you see! But you have no idea they are even there. But if you have a radio you can “capture” the radio waves. The antenna will “perceive” those waves and then the radio will translate those into a sound (a different wave). Your brain is very much like a radio. Your eyes are like antennas, they will perceive light waves (not luminous remember! just dark waves, just like radio waves: they are the same thing, just different energy/frequency) and your brain, just like the radio, will convert those waves into images. Images are a product of your brain. They are completely artificial constructions that have nothing to do with the true nature of the light that your brain used.

So, to answer your question: No, as long as you have a brain you’ll never “experience” the universe. We can see images that reflect the distribution of phenomena that’s actually out there, but those images are not the essence. The essence is just dark waves and fields and interactions. The universe we experience is far more beutiful than the actual thing. We transform meaningless dark waves into beautiful sounds, and pictures. You can look up to the sky and see the beauty of the milky way or the omnipotence of the sun during the day. Be happy with your fake experience as without that, there’s nothing to see.

Very true that we don't know what caused the Big Bang and we probably will never know. The answer of "infinity" was just silly. But if you are interested look at Brane Cosmology and the Multiverse hypothesis.

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If, as you say, humans have a vastly limited understanding of reality, and you are one, how would you know or recognize reality if you saw it or were experiencing it?

And no amount of belief makes anything true. If true, truth is true without your belief. In other words, truth doesn't care if you believe.