Looking at the New Testament in the Greek language original offers some fascinating translations or interpretations. A favorite reference book I use is Word Study Greek-English New Testament, edited by Paul McReynolds. Since I don't know classical, New Testament, or modern Greek, I'm either unbiased or dangerous, so be forewarned and see if my interpretations are logical.
Hebrews 11:1 is usually translated, "Faith is the assurance of things hoped for, the conviction of things not seen." (NASB). Let's look at the Greek. The word translated faith is pistis, which can also be translated as trust. That in itself could make a sermon. Faith is trust. Have faith in God means have trust in God. But let's go on. The word translated assurance in the NASB is alternately translated as substance in other versions. However, the Greek behind it is hypostasis which means, literally, standing below (hypo = below, stasis = standings). Thus, another word that fits hypostasis is foundation. That would make Hebrews 11:1a read, "Trust is the foundation of our hope."
Since Hebrews 11 is about faith, let's continue with the translation of 11:1a as, "Faith is the foundation of our hope." Then the remainder of 11:1. The Greek translated conviction or evidence is elegchos, meaning rebuke, reprove, expose. What literally says, "rebuking invisible things" means to give an answer for, or refute. It's like a response in a debate, a rebuttal. So, a clear translation of Hebrews 11:1b requires some rewording, but the usual word translated from elegchos should not be conviction or evidence, in my view. I would translate it this way:
Faith is the foundation of our hope, our confidence in the truth of things we can't yet see.
Faith provides the anchor of confident trust in God's truth when you can't see, know, or understand yet.