I can give you an actual and irrefutable proof but it does not have to be empirical.
Science cannot prove the existence of God. But science cannot disprove it either. So I think it is very unwise to ask for scientific proofs.
Philosophical proofs are very good proofs but they do not have to be scientific.
Philosophically speaking, to say "There is no God" is an example of an absolute statement. For one to be qualified of an absolute statement, one must have absolute knowledge. Another example of an absolute statement is "There is no gold in the US." For you to say that you must have searched all of the US, its territories and its inhabitants. If in your thorough search you found nothing, then you have absolute knowledge and is capable of saying "There is no gold in the US." It is the same thing with our original absolute statement. Before you say, "there is no God," you must have searched everything and everywhere that God can be found. You must have searched the sun, the planets, the moons, the other galaxies, the whole universe and all of its inhabitants. If you have not, then you are not qualified to say an absolute statement like that. i have not heard anyone who have done that so NO ONE is qualified to say "There is no God".
On the one hand, to say "There is a God" does not require you to have absolute knowledge. It is the same thing with saying "There is a gold in the US". The thing here is one have to have credibility to say that. In order for one to have credibility, one must have done their searching.
Since we just disproved the statement "There is no God". There must be one. But which one?
There is this great philosopher named Thomas of Aquino who wrote and explained the existence of God.
The Five Ways (Quinquae viae)
1. The Argument from Motion (Ex Motu)
a. Nothing can move itself
b. If every object in motion had a mover, then the first object in motion needed a mover
c. Therefore, there is an unmoved mover from whom all motion proceeds.
d. This first mover is the Unmoved Mover, called God
2. Causation of Existence (Ex Causa)
a. Some things are caused
b. Everything that is caused is caused by something else
c. Therefore, there must be an uncaused cause of all caused things.
d. This causer is what we call God
3. Contingency and Necessary Objects (Ex Contingentia)
a. Things in the universe may either exist or not exist. Such things are called contingent beings
b. Not every being can be contingent. It is impossible for everything in the universe to be contingent, as nothing can come of nothing, and if traced back eventually there must have been one thing from which all others have occurred
c. Therefore, there must be a necessary being whose existence is not contingent on any other being
d. This being is what we call God
4. The Argument from Degrees and Perfection (Ex Gradu)
a. Various perfections may be found in varying degrees throughout the universe. An example is two marble sculptures, one is beautiful than the other. Comparing these two objects, one has a greater degree of beauty than the other. This is referred to as degrees or gradation of quality.
b. These degrees of perfections assume the existence of the perfections themselves. Thomas of Aquino concluded that for any given quality (e.g. goodness, beauty, knowledge) there must be a perfect standard by which all such qualities are measured. These perfections are contained in God.
5. The Argument from Intelligent Design
a. All natural bodies in the world act for ends.
b. These objects are in themselves unintelligent.
c. To act for ends is characteristic of intelligence.
d. Therefore, there exists an intelligent being which guides all natural bodies to their ends.
e. This being we call God
Thomas of Aquino, say that there is a God. As a thinker myself, I truly believe that he is credible to say that. It has led me to believe that there is a God. But which one? Thomas of Aquino did not stop there, he wrote the whole Summa Theologica for the Catholic Church. He was a Catholic priest in the Order of Preachers in the 13th Century. He was also named St. Thomas Aquinas.
I am a Catholic. I believe in One God, the Father, the Son and the Holy Spirit. I am just trying to help you out.
Ad Majorem Dei Gloriam
Edit: "Well if so, then he can't be measured by proof, because then he would no longer be immeasurable or limitless, and thus not God"
Do not absolute proofs as only empirical there are also more proofs like philosophical ones. I am talking of a philosophical proof which is knowledge. Knowledge itself cannot be measured.