The Hawks began life back in the National League South with a 1-1 draw against Welling United at Westleigh Park.
Roarie Deacon gave the hosts a 12th-minute lead, before Adam Coombes levelled six minutes before half-time.
Although the Hawks dominated the second half, they failed to break down a resilient Welling defence.
Andy Drury fired in the first shot of the season with a 20-yard volley straight at goalkeeper Dan Wilks.
Wes Fogden picked up a seventh-minute booking following a challenge on Sanchez Ming.
On 12 minutes the Hawks got the dream start they wanted when they opened the scoring in their first real attack.
Jonah Ayunga threaded a lovely ball through to Deacon on the right of the Wings’ area.
Deacon took the ball in his stride and fired his shot low across Wilks into the bottom far corner of the net.
Almost immediately Nicky Bailey smashed a free-kick from outside the area narrowly over the top.
Eight minutes before the break it took a superb low one-handed save from Wilks to prevent Ayunga extending the home side’s lead.
Two minutes later Welling grabbed an equaliser.
Goldberg played in Coombes who easily beat keeper Ross Worner from close-range.
At the start of the second period Ayunga sent a curling cross bouncing against the crossbar with Wilks well beaten.
Drury delivered a superb ball into the area for Ayunga, who sent his close-range volley at the keeper.
The Hawks started to put the visitors under a sustained spell of pressure.
Josh Taylor fired inches past the far post as the home side domination increased.
Fogden set up Ayunga with a great shooting chance - but the striker fired high and wide.
The home side made a double change with 14 minutes remaining by sending on Alfie Rutherford and Bradley Tarbuck for Drury and Taylor.
And although Doswell’s troops applied late pressure they couldn't find a way through a resolute Welling rearguard.