If you keep the gravity low - 1030 or so, use extract, irish moss, a highly flocculating yeast and maybe finings or filtering too you might get something if you're not too fussy about cloudiness. I'll often have a half pint of the brew when transferring from primary and it can taste ok, it just looks like soup.
Here's a light ale recipe I did way back in the days before moving to grain you could hold back 250g of the extract to get it to 1030.
For 12l - OG 1040
1.5kg pale malt syrup
120g amber malt - steep at 90C for 30 mins and add liquid to boil
Irish Moss.
Hops
Challenger 20g 90 min
Kent Goldings 20g 90min
Hallertau 10g 10min
No note on the yeast so it was probably just generic 'english ale yeast'
According to my notes it hit Fg 1020 in 5 days and tasted fine.
These days I'd put a shedload of hops in at the end of the boil too.
Plenty of cheap breweries ferment fast, filter and force carbonate young beer, they won't win any awards but it's drinkable enough that they stay in business so it might be worth a go.