Abraham exercised faith by believing. But it isn't mental gymnastics. "Faith comes from hearing, and hearing by the word of Christ" (Ro 10:17). "By faith we understand that the worlds were prepared by the word of God" (Heb 11:3). Even though "what is seen" (:3) is visible they were "not made out of things which are visible" (:3). It requires faith to accept this. "For by grace you have been saved through faith" (Eph 2:8). "It is by faith, in order that it may be in accordance with grace" (Ro 4:16). "It is the gift of God; not as a result of works, so that no one may boast" (Eph 2:8-9). It was a promise that Abraham "would be heir of the world" (Ro 4:13) and faith ensures "that the promise will be guaranteed" (:16).
Hebrews 11:1 defines faith because it says "faith is." If the text consisted of metaphors they would be likenesses, but one part says "faith is . . . the conviction of things not seen" (11:1) which is more of a definition. We weren't witnesses when "the worlds were prepared by the word of God" (11:3) but "that which is known about God is evident within them; for God made it evident to them" (Ro 1:19) and "His invisible attributes . . . have been clearly seen" (:20). This evidence is not unlike what is presented in a court case which substantiates the truth. You see the reality of what had been previously unproven when it is spelled out by God through faith. Faith is the tangible evidence which comes only from God.