The Baggies currently sit 16th in the Premier League, three points above the drop zone, ahead of their crucial home clash with fellow relegation strugglers Cardiff on Saturday.
After spending most of the season on the sidelines, Dawson has come into the side for the last two games - a 2-1 away win at Swansea followed by a 2-0 defeat at Hull City.
The 23-year-old - who was signed by home town club Rochdale in 2009 from Radcliffe Borough and then moved on to West Brom the year after - says being rejected as a 16-year-old has toughened him up for battles ahead.
"I'd been knocked back by Bolton Wanderers and Rochdale,'' Dawson told the Daily Telegraph.
"They were tough times. I thought: 'is this it?' I definitely thought football might not work out for me. But I went running before school and after school, thinking: 'Right, I'm going to work harder, get fitter and stronger and try my best to prove all these people wrong'.
"I'd be up at 7am, running round Rochdale for 40 minutes before school. I went out in the dark, running under street-lights, not many people about, a few cars. My family supported me a hell of a lot because not getting a contract was difficult to take at 16 but a lot of it came from me pushing myself. It made me tougher.
"When it's tough here I remember those days running before school and playing in non-league and that makes me dig in and work even harder."
Dawson has backed Spanish head coach Pepe Mel to keep the Baggies up, insisting there is belief in the squad.
"He's a great guy. It's been difficult for him with the language barrier but he has been working with Keith (Downing) and Dean (Kiely) to get the message across.
"Everything we do on the training pitch is geared to winning games. The lads are definitely positive we can stay in the Premier League.''