I'm not a master deckbuilder, but I might be the first to post in the thread here.
You have Data and Destiny, and two core sets, so you have lots of really good NBN cards.
SYNC seems to be least impacted by cards you are missing. Traditional Sync protects R&D, HQ, and one scoring remote with lots of Ice that only tags the runner, but is very expensive to break with icebreakers it runs just enough copies of operations that punish the runner for taking tags that accepting the tags is not worth it for the runner.
I tried to adjust the standard build to account for different elements of your collection, although a Sync expert might disagree on what direction to take.
SYNC: Everything, Everywhere (Data and Destiny)
3x AstroScript Pilot Program (Core Set)
3x Quantum Predictive Model (Data and Destiny)
3x Global Food Initiative (Data and Destiny) •••
3x Adonis Campaign (Core Set) ••••• •
1x Melange Mining Corp. (Core Set)
3x News Team (Data and Destiny)
1x Disposable HQ (Business First)
1x SanSan City Grid (Core Set)
1x Keegan Lane (Data and Destiny)
1x Archived Memories (Core Set) ••
1x Closed Accounts (Core Set)
1x Psychographics (Core Set)
3x Hedge Fund (Core Set)
1x Wall of Static (Core Set)
3x Resistor (Data and Destiny)
Code Gate (5)
2x Tollbooth (Core Set)
1x Enigma (Core Set)
2x Archangel (Data and Destiny)
3x Data Raven (Core Set)
2x Turnpike (Data and Destiny)
1x Assassin (Data and Destiny)
11 influence spent (maximum 15)
18 agenda points (between 18 and 19)
40 cards (min 40)
Cards up to Business First