Short of actually being able to understand and verify every single piece of data that has gone into proving it - like it or not you take it on faith. Faith is a measure of trust in your sources in the same way that people respond differently to news from different outlets. I can walk outside and prove gravity. I cannot do the same with evolution.
The basic fact of most information we receive on a daily basis is that we trust it until we have a reason to question it. Evolution has zero effect on the daily lives of anybody outside of investigative curiosity. If somebody has their life changed by God (and it happens all the time) they'll spend a huge part of the rest of their lives searching for answers and understanding...and that will give them cause to question evolution because the Bible makes a tremendous amount more sense when reading it AFTER something like that happens to you. If you're not the slightest bit religious, you have no reason not to simply accept it because it doesn't affect you at all. Plus you can use it as a cognitive tool to reinforce your belief that religious people are all simply dumber than you because they don't fully agree with something that you claim to know as a fact, even though you're simply trusting your sources.
I generally don't bother arguing the point because people don't accept information that contradicts their world view and being able to verifiably prove something from that perspective from one side or the other won't have any affect on the lives of...anyone. It's just something useless to argue about. Getting into "arguments" where nobody is going to change anyones mind and you believe you are correct serves no other purpose than to boost your own ego.
Try to wrap your mind around this and see it from another perspective. If you KNOW God is very real (not believe; God has directly impacted your life in a tangible way...you KNOW) then come at the question from that side. If you know God is real your entire perspective on the Bible and everything in it changes specifically because any questions you may be able to have about it to try to cast doubt on its text go out the window...because ultimately you know the most important part of it is very real and that changes your entire perspective on it.
One of my favorite quotes:
"The test of first rate intelligence is the ability to hold two opposed ideas in the mind at the same time and still retain the ability to function." - F. Scott Fitzgerald
Many people like to assume that people just go sit in a service or read a book and are magically convinced to believe. That's naive. There is also this idea that people lack the critical thinking to question it. That's also naive since those questions are the first thing that everybody asks. It takes a lot of ego to assume every single person in those pews hasn't questioned it, strongly. Especially the ones who donate huge sums of money to it.
The reality is that life change happens much more often than most people would like to admit and hearing enough people you know give testimony about that life change creates trust in the information, even if it has not happened to you personally yet. This is buoyed by the fact that those people are telling you this because they want you to be able to receive the same help that they did. There is no financial motive. There is no other incentive than sharing their experience of something they didn't previously believe which they now feel obligated to express for the betterment of those around them.
Writing those people off, however, takes a tremendous amount of hubris. I never take any issue with a person who has questions. I only take issue with people who think they have all the answers.