HaloRuns tracks New Game+ speedruns, meaning you may collect audio logs before the run. However, you must still start on Prepare to Drop, as it is the narrative beginning of the game.
For New-Game speedruns, using a temporary profile, you must collect 8 audio logs during the run to unlock use of Mongooses in Mombasa Streets. See the route below.
To avoid combat on Mombasa, just run/drive past enemies. They aren't allowed to leave the specific sections that they spawn in and can't follow you.