If your wife is a Nicaraguan passport holder, then yes, she may benefit from the CHNV program. She cannot apply herself. You (the sponsor) will need to file I-134A for her. If she is granted the single-entry travel authorization, she may travel to the US with that document, be paroled in, then apply to adjust status in the US based on marriage to you, a US citizen.
There's no guaranteed timeframe for I-134A processing due to high demand. It's partially via lottery system now. From the USCIS page you linked above -- "Due to high interest in these processes, we are updating the review process effective May 17, 2023. Under the new review process, we will randomly select about half of the monthly total of Forms I-134A, Online Request to be a Supporter and Declaration of Financial Support, regardless of filing date, from the entire pending workload to review. We will review the other half of the monthly total of Forms I-134A based on when the case was submitted under the first-in, first-out method, which prioritizes the oldest Forms I-134A for review."