I don't fully understand what Christians mean when they say "have faith in God and trust in God."
Essentially everything we know about God has been communicated through man. Thousands of years ago men compiled a book that tells us everything that God is. It tells us that he is loving, faithful, forgiving, all-powerful, eternal and our only hope for salvation. So when Christians ask a skeptic to put their faith in God, who are they really asking the skeptic to put their faith in? God or man? Doesn't a person need to first put their trust into the source of all this information (man himself)?
I can see what you mean here, however I believe there is a misnomer in the phrasing of your question: it **seems** to presume that God has had no direct contact with any human being, and thus all the information there is about "God" exists due to mankind spreading the word to each other, more or less.
You probably would agree that Obama is a real, living person, who actually is the current POTUS. Thus, it's possible to know him personally, meet with him, etc. The chances of you getting to do that may be slim, however it is **possible**. Also, there are those who act under his orders, who speak on his behalf to varying degrees (which he either approves or doesn't approves), etc.
Now, if no one had ever seen Obama, and all we had to go on was the word of others, documents with his signature and quotes by him, etc ... you would have a group of people who believed he existed, and those who do not. In fact, I'm sure there is a group of people who probably believe he doesn't exist, he's just an actor, or perhaps a digital creation, etc (think conspiracy theory, like faking moon landings, etc). However if no one had laid eyes on him, and all we had was the word of others and things in his name but never the man himself ... then people's beliefs would largely rest upon each other and what little evidence there was even for his existence. However, since there is a man running around named Obama who many have met, with lots of historical evidence testifying to his existence and role as POTUS ... it doesn't take a huge stretch to believe he actually exists. It's essentially on the level of fact. I mean, I've never personally met Obama or seen him in person, but I'm going to say that I assume he actually exists lol.
In your question, it seems like your presumption is that no one has ever seen or interacted with God personally. All they have are letters, the words of others, a belief He either exists or He doesn't exist, etc, but no personal experience. However there are plenty of people all throughout history who claim to have personal interaction with an entity they recognize or call "God", or experiences or personal interactions with things they attribute to the supernatural/paranormal/etc that sometimes get attributed to a version of God as well. For those people, one could argue they are not placing their faith in something they have only heard about through others, rather they are witnesses to **something** that they either chose to believe was "God" for some reason, OR WHAT THEY EXPERIENCED CLAIMED TO BE GOD with them. Obviously some of those experiences are more mundane and harder to attribute extraordinary explanations to than others, and some of them contradict each other as well, but regardless, they are there and there are people who claim such things, regardless of what their claims turn out to be or not, and whether they end up explained or remained unexplained by the majority.