First of all, I concur with Alvin Plantinga who calls belief in God, a properly basic belief. Nevertheless there are good reasons to believe in God. I don't call it "evidence" in the sense of "scientific evidence", i.e. using the scientific method, as it is defined and limited to empirical data, which excludes spirits, disembodied minds, extra dimensions, metaphysics and the like.
This limitation imposed through the science method speaks as to its general inadequacies. For example, science cannot prove or validate the scientific method. This was known as Positivism, and has been weighed in the balances and found wanting. The scientific method cannot prove that I exist apart from my body, nor can it prove that I exist apart from my mind (in a sort of matrix or dream). These are, however, properly basic beliefs. If you are a materialist (physicalist), you would obviously take issue with the former, while recognizing the latter.
What I'm saying is that by the very attributes of God, as defined in Holy Scripture, and the limitations of the scientific method, it's a misunderstanding to suggest "scientific" proof for the existence of God. We're not going to produce God's body or pieces of it to examine, because God is spirit. We can, however, look at our physical world and ourselves, and explore their nature, how they function, their origins and through scientific observations, make reasonable conclusions, through deductions and inductive arguments.
The following is part of a growing list I've been working on. I actually lost my first list and started working on a new one. The arguments come from numerous sources, including Alvin Plantinga, C.S. Lewis, Francis Schaefer, William Lane Craig, J.P. Moreland, Vishal Mangalwadi, Peter Kreeft, Dinesh Desouza, etc.
Here's a few of them:
The cosmological argument,
The teleological argument,
The argument from design,
The moral argument,
The argument from efficient causality,
The argument from contingency,
The argument from consciousness,
The argument from meaning,
The transcendental argument,
The ontological argument,
The argument from reason,
The argument from human dignity,
The argument from pragmatism,
The argument from human flourishing,
The argument from physical constants,
The argument from simplicity,
The argument from the origin of life and its evolution,
The argument from self,
The argument from natural laws,
The argument from the resurrection,
The argument from evil,
The argument from love,
The argument from justice,
The argument from æsthetics,
The argument from purpose,
The argument from miracles and providence,
The argument from human spirituality and religious experience,
The argument from religious need,
The argument from joy,
The argument from near death experiences and consciousness after death,
The argument from changed lives,
The evidence of fulfilled prophecy,
The argument from coherence,
I think that the existence of God is the best explanation to each of the above, and I find the accumulative case to be quite overwhelming.
In contrast to theism, I find naturalism/materialism to be incoherent, inherently restricting possibilities and scientific progress, contradicting human experience and impossible to live out consistently, while Christian theism provides an opportunity for personal growth, social order and paves the way for scientific progress.
For example, it was within a Christian context that slavery was abolished, even though it was one of the oldest and most globally established practices, even within early Judaism. But, it was Christians, such as William Wilberforce who heralded the call for its abolishment. Furthermore, with the rise of scientific progress in combination with state mandated "scientific" atheism, we have seen the most depraved human acts ever devised against other human beings. Science without God, not only closes the mind, it lacks the moral compass by which to judge right from wrong and denies human dignity. We can actually see this played out in many of the hateful debates online. Sadly, I have also seen Christians to take part in the insults and name calling. We will never win anyone with such disparaging remarks.
Christians should never be ashamed for believing in God, and following Christ. May God give us the grace to live out loud!