This statement comes in the context of explaining the unbelief of people who have access to God's revelation of Himself, but who continue in their unbelief.
"Let God be true, but every man a liar," answers a charge against God - that somehow the unbelief of men is God's fault. Has God's word been ineffective? Have God's promises been unfulfilled? Is God not capable of accomplishing His will and His plan? Has God not done enough? Is God not capable of doing enough? Is God's word true and trustworthy - or not?
This is where many people live. They claim they would believe if God would only give them a sufficiently clear sign. Could not God speak to them from heaven, or appear to them in person, or bring about a miracle to satisfy their skeptical heart? If He can, but He doesn't - how can He be good? If He cannot - how can He be God? So people feel free to ignore God in their lives.
But God says, by His word here, that He has given people the truth. The truth is apparent. The truth is authoritative. The truth is enough.
(Romans 1:18–20) For the wrath of God is revealed from heaven against all ungodliness and unrighteousness of men, who suppress the truth in unrighteousness,
19 because what may be known of God is manifest in them, for God has shown it to them.
20 For since the creation of the world His invisible attributes are clearly seen, being understood by the things that are made, even His eternal power and Godhead, so that they are without excuse,
People don't want a sign from God - they just use that as an excuse for ignoring the truth in their unbelief. It is a sleight of hand - a misdirection - by which they divert attention away from the fact that they categorically and willfully reject what they do know about the God of the Bible. No matter what sign they were given, they would still reject God in willful unbelief.
(John 3:19) And this is the condemnation, that the light has come into the world, and men loved darkness rather than light, because their deeds were evil.
God is not confused by sleight of hand. He is true - even if all humans everywhere joined together in unbelief. God is true and will judge according to His truth. At that judgment, God will be vindicated as Holy. Unbelievers will receive perfect justice and finally acknowledge God as true.
(John 16:8–11) And when He [The Holy Spirit] has come, He will convict the world of sin, and of righteousness, and of judgment:
9 of sin, because they do not believe in Me;
10 of righteousness, because I go to My Father and you see Me no more;
11 of judgment, because the ruler of this world is judged.
(John 14:6) ¶ Jesus said to him, “I am the way, the truth, and the life. No one comes to the Father except through Me.
(Philippians 2:9–11) Therefore God also has highly exalted Him and given Him the name which is above every name,
10 that at the name of Jesus every knee should bow, of those in heaven, and of those on earth, and of those under the earth,
11 and that every tongue should confess that Jesus Christ is Lord, to the glory of God the Father.