Five Northern Premier League clubs feature in the draw, although all face fourth qualifying round replays on Tuesday night to ensure their progress.
Marine, who famously made it to the third round proper last season, face a trip to EFL League Two side Harrogate Town if they can beat Wrexham.
Two NPL sides could potentially face each other in the first round. Both Buxton and Morpeth drew away at the weekend and face Kettering Town and York City respectively at home on Tuesday, with the prize a clash in the next round.
Pontefract Collieries, who celebrated a club record crowd against FC Halifax Town at the weekend, will host Maidenhead United if they can upset the odds away at The Shay on Tuesday.
NPL East Division side Marske United travel to Gateshead for their replay with a home tie against Altrincham at stake.
Up to six first round fixtures will be selected for live television coverage in the UK, with a possible further eight ties selected for other broadcast coverage.
Full FA Cup first round draw (NPL clubs in bold):
Bradford City v Exeter City
Sunderland v Mansfield Town
Dorking Wanders or Hayes & Yeading United v Sutton United
Sheffield Wednesday v Plymouth Argyle
Dagenham & Redbridge v Salford City
Carlisle United v Horsham
Dover Athletic or Yate Town v Yeovil Town or Weymouth
Scunthorpe United v Doncaster Rovers
Rotherham United v Bromley
Portsmouth v Harrow Borough
Gillingham v Cheltenham Town
Morecambe v Newport County
Banbury United v Barrow
Fleetwood Town v Burton Albion
AFC Sudbury v Colchester United
Northampton Town v Cambridge United
Corinthian Casuals or St Albans City v Forest Green Rovers
Boston United or Stratford Town v Shrewsbury Town
Pontefract Collieries or FC Halifax Town v Maidenhead United
Chesterfield v Southend United
Rochdale v Tamworth or Notts County
Kidderminster Harriers v Grimsby Town
Wigan Athletic v Solihull Moors
Boreham Wood v Eastleigh or Folkestone Invicta
York City or Morpeth Town v Kettering Town or Buxton
Ipswich Town v Oldham Athletic
AFC Wimbledon v Brackley Town or Guiseley
Harrogate Town v Marine or Wrexham
Hartlepool United v Wycombe Wanderers
King’s Lynn Town v Walsall
Crewe Alexandra v Swindon Town
Bolton Wanderers v Stockport County
Charlton Athletic v Torquay United or Havant & Waterlooville
Oxford United v Bristol Rovers
Crawley Town v Tranmere Rovers
Leyton Orient v Ebbsfleet United
Milton Keynes Dons v Stevenage
Lincoln City v Bowers & Pitsea
Port Vale v Accrington Stanley
Marske United or Gateshead v Altrincham