He impressed new director of rugby Lyn Jones with his natural talent and worth ethic and has since signed a three-year professional contract that will see him remain at Rodney Parade until the end of the 2016/17 season.
The former Wales U16, U18 and U20 international has gone on to play 25 times for the Dragons since his debut against Ulster in the season opener, missing just three games in all and starting on 15 occasions.
His rapid rise was mirrored by that of the squad as a whole early on in the campaign, with the Dragons getting off to flying start under Jones' guidance. And, while that progress in terms of results has slowed somewhat since the turn of the year, Screech is convinced there is plenty to look forward to as the Dragons target a strong finish to the season.
"I've exceeded a lot of my expectations this year," said Screech. "Earlier in the season I was just hoping to be involved in the next game, but I've been lucky enough to be involved in almost every game, and I'm loving it. Hopefully it carries on.
"I've had ups and downs during the season but on a whole it's been a pretty good season. At the start of the year I didn't have a Dragons contract, I was at Bedwas with a chance to train with the Dragons. Then Lyn wanted to sign me for three years on a professional contract which I was delighted with.
"I've learnt a lot from Adam Jones and Duncan (Bell) this year, and with Ian Gough coming, in as a Welsh international who has played in England, I'm hoping to learn a lot from him as well.
"We wanted to lay the ground works this year with a view to us becoming one of the top two regions in Wales. I think since Lyn has come in, the Dragons have improved a lot and next year, with another good pre-season and with a couple more experienced players, we can push on to achieve that."
The Dragons have won just once in the RaboDirect PRO12 since the beginning of January but there is still plenty to play as they get set to take on Treviso at the Stadio di Monigo on Saturday.
Screech and co currently sit ninth in the standings, three points above the 10th-placed Cardiff Blues having played the same number of games, and a strong finish could easily see them finish above both Connacht and Edinburgh despite their recent defeats to those two teams at Rodney Parade.
"We had a good look at ourselves after the Connacht game," added Screech. "We decided that we needed to work harder and not let it happen again because it was embarrassing against Connacht. We're trying to improve in the last four games of the season.
"We've put a lot more focus on our drive since Connacht. I thought we were pretty good against Zebre (they drew 25-25 in Italy) - it was one of our better performances in the tight.
"This will be my first time playing in Treviso and I expect them to be forward orientated, but I think we've taken a big step forward in the last two games since the loss to Connacht and hopefully we can go further again against Treviso this weekend.
"We've got four games left and we want to win them all. The league is close and we have dipped into the lower bracket recently, but if we get a couple of wins, hopefully it will stand us in good stead."