Aurelion Sol, specifically in the jungle, offers:

Incredble chase down potential
Flexible and omnipresent gank opportunities
Almost unprecedented scaling
Tank melting, squishy farming
Rapid stardust acquisition with ganks and camps

Now, Aurelion Sol, specifically in the jungle, suffers from:

Early invasion vulnerability
CC of any form
Extremely mobile champions

Our first weakness is addressed by scaling, while our second can be mitigated with our summoner spells and Banshee's Veil; our final weakness is minimized by Rylai's Crystal Scepter. If Aurelion's glaring strengths appear to the reader to outshine his aforementioned sensitivities, I would encourage them to proceed, and eat from the tree of DRAGONFRUIT.

Short answer? Prioritize your stardust stacks while farming and ganking.

Aurelion hits considerable power spikes, in his dueling and his farming rates, at levels 6 and 9. Prior, one should emphasize clean farming (balancing camps' health and your E cooldown management to receive all stardust stacks on monster deaths within its window), and map awareness. Have your allies ward red buff, and anticipate an invasion almost immediately. Starting blue is essential, to avoid mana problems before you can afford your tear, as well as to reach level 3, and upgade Q to level 2, facilitating a full clear, with all stacks, within 3:30. This is possible with a sufficient leash (30% hp). Without one, it is absolutely necessary that you back after murk wolves to purchase a Tear.

Invasions should be considered out of locational convenience, safety, and ability, prioritizing, in order:
Raptors >> Krugs >> Murk Wolves >> Blue Buff
Make a habit of requesting that your mid-laner ward the enemy raptors, for a quick 7 stacks whenever it becomes available. Ganking is almost always feasible and desirable after a full clear, expediting our star dust acquisition, and stacking our keystones in the case of First Strike and Dark Harvest. In some cases, it is preferable to wait for, or force a gank, than to clear blue-side camps, simply because more stardust is acquired with a few seconds of E and Q contact with enemy champions than is gained from defeating Gromp and the Murk Wolves. With this in mind, it is entirely possible to have over 90 stacks by the 10 minute mark, and 200 stacks by the 16 minute mark.

Objectives should NOT be attempted without adequate vision and team support. Prioritize dragons, and the dragon soul, over heralds and grubs.

Your W end location when ganking should resemble a line of best fit over their possible escape paths. Don't hesitate to recast as soon as their path starts to diverge from your own. Maximize the time they spend under your Q in every possible peel sequence (Q boasts a remarkable range, that only grows with level. Be mindful of this when skirmishing and the like). Similarly, E in front of your targets, not upon them, and for the sake of Allah, don't miss your R. Most importantly, do not underestimate your own damage output. In lieu of an attending ally, vomiting constellation concentrate is a sufficient and often lethal deterrent to any pursuing parties.