Assistant captain Richard Bostock said: “When we saw the fixtures we knew we definitely had a chance of being in this position.
“We don't play anyone from last year's top four for another two weeks and we knew the others had to play each other.
“So we knew if we really stuck to it and started well then we would be in this position and it's now about taking that momentum into next weekend.”
Attenborough won the toss and elected to bat first in what became a very high-scoring encounter, making 295-8.
Openers Ben Shaw (73) and Savin Perera (129) combined for a solid 199 opening partnership with David Freeman adding 38, Bostock taking 3-57.
The home side also produced a fine opening partnership of 92 between Nidck Keast (59) and Ewan Laughton (39).
There was also solid scoring from the next four batsman as Nick Langfod added 26 before Tom Ullyott (64) and Joseph Hayes 962) made 95 for the fourth wicket.
Josh Porter also scored 31 as Cuckney reached 298-6 in 45.3 overs.
“The plan was always to bowl first as there was a little bit of damp around in the morning, but it turned out to be a really flat wicket and didn't offer a lot to the bowlers, especially the seamers, in either innings,” said Bostock. “So they set us a big chase. But we knew at home if we stayed with the rate, we'd be there or thereabouts - and we got over the line.
“It was fast scoring and the ball came on nicely. Both opening partnerships batted really well and took advantage of any stray deliveries.
“Everyone chipped in. On big chases you either need someone to get a massive score individually or everyone needs to be at the races, and that's what we did.”
Cuckney will now try to extend their winning start away at Wollaton this Saturday.
“Wollaton are an established Premier League team and we know what they're about, especially at their place,” said Bostock. “They have the leading wicket taker, Zain Latif, for the past two years so they are definitely dangerous, especially at Wollaton.
“So we won't be taking anything for granted, but we will be going there looking to win.”