As the attackers, try taking the route on the right. Characters with movement abilities, like Pharah, Genji, Widowmaker, and D.Va, can get over a short wall and into the courtyard. If the payload is stuck under the archway, it’s a good way to flank.
Use D.Va or Pharah to sneak around to the left of the final point and flank the defenders.
It’s possible to triple Tracer blink from the corner of the map near the first capture point around the edge of the cliff to the corner of the second bend on the payload track. It’s tricky to pull off at first, so practice before trying to use it. It’s much easier, of course, for Pharah, D.Va, or Lucio.
Pharah and others can take a less-direct approach to the dig site by going over the ledge and around. Nothing special, but it can help.
Lucio can run around in the big hole for as long as he likes. Do it long enough and someone will shoot you.
In the Village part of the map, Pharah and D.Va can easily skip around to the outside of the map to get to the wooden walkway at the side of the point.
The same goes for the Shrine point.
In the Sanctum portion, characters with movement abilities can easily get around on the ledge outside the point. Surprisingly, Soldier: 76 can use it to flank, too.
Pharah can exit and enter both of the spawn points in one of the rounds by flying around the buildings that block off one side. Turn your back to the gap, jump a little, and fire E to propel yourself toward the corner of the buildings. Then hold Space to stay afloat, and use Shift when you’re close enough to the other side to make it over. It's a quick way to get to the point or flank the other team, but it uses up both your abilities, so it’s not super practical. (It's cool though!)