Now fully recovered, Hay is determined to enjoy a prolonged run in the side.
Hay said: "I'm happy to be back in training and I played for the reserves on Tuesday. I've felt good in training and although I won't be match fit for a while it's great to be back.
"It's been a nightmare start for me. I was fit all pre-season, played all the games and everything was great but then 50 minutes into the Celtic game I felt a tug in my hamstring.
"It didn't feel that bad and since I came straight off I thought I'd be out for just three or four weeks. That turned out to be the case as I came back for the Peterhead game and thought everything was okay but I wasn't yet 100%.
"I really tore it in that game and it was quite a bad tear and that was about eight weeks ago.
"I've played half a game against Celtic and half a game against Peterhead since the start of the season.
"The physio Alex has been great. After the Peterhead game he said I'd be out for six to eight weeks but we erred on the side of caution, giving me as long as it takes. He didn't push me too hard and just made sure my rehab was right."
Killie have toiled in recent weeks as Jim Jefferies' side have been hampered by injuries but Hay is convinced they can force their way into the top six for the third successive season.
He said: "We're just reaching the end of the first quarter of the season and our aim is always to get into the top six.
"We're looking to go on a run of results but we'll certainly give it a go."