Does God exist? Why should I believe there is a God? I’m a fallen-away Catholic who has recently read many books on an anti-Christian subject, evolution, and similar topics but I have many problems with evolution,too. I guess you could call me an agnostic right now.

I have a few concepts I would like to provide.
Regarding God’s Existence
Could you accept any one or more of the following? These are simplified and personal understandings of Thomas Aquinas’ Proofs of God’s Existence in Summa Theologica.
a. Things that are in movement required a mover. Therefore, the expanding universe required an initial mover, which itself did not require a mover. This initial mover is called God.
b. Actions have causes. Therefore, the thing credited with the first cause, without itself requiring a cause, is called God.
c. Things have qualities of good, bad, righteous, wrong, true, false, and the like. Therefore, there is one thing that is the best, truest, most righteous, most merciful, etc. This perfect being/state is called God.
d. If a being lacks intelligence, it cannot desire an end result which requires fuller intelligence, unless it is directed by something of fuller intelligence. Since we know and desire something that is greater than our understanding and know how, we must be directed by something of fuller intelligence. We say God is the being providing the direction.
Regarding “Why believe in God?”
Because “Always being patient and kind towards God with all your heart, mind, strength, and soul and towards others, as towards yourself, as Jesus did, according to Scripture, as understood by the Church,” is the best solution to achieving the greatest peace, happiness, energy, knowledge, and understanding for any being and/or society regardless of age, gender, intelligence, economic status, culture, etc.
My recommendations:
If you want the fullest peace in your life (including spreading peace to all others), learn the best patience.
If you want the fullest happiness (including spreading happiness), learn the best kindness.
If you want the fullest energy (including spreading energy), learn to be motivated for God.
If you want the perfect role model, follow Jesus.
If you want more info about Jesus, learn Scripture.
If you want greater understanding of Scripture and Jesus’ Ways, learn Catholicism.
I hopes this helps draw you closer to God. I greatly appreciate you asking these thought-provoking questions! I look forward to hearing your thoughts.