Actually - you cannot - unless you have a canoe.
There are stretches in northwest Ontario where there is no option except the TCH.
However, there are plenty of options elsewhere.
Machka can be a big help in Alberta.
Consider taking Highway 20 out of Bella Coola.
There is a murderous climb over Heckman Pass
but the road is mostly paved after the pass and very lightly traveled.
Hwy 20 connects with Hwy 97 at Williams Lake.
You can stay on pavement cutting south to 100 Mile House
Then over to Clearwater and up Hwy 5 to Mount Robson
Or you can use back road to Quesnel, Hwy 26 to Wells
Then forest roads up to Purden Lake to Hwy 16.
Regardless of which way you do it, you have to cross the Rockies on a highway.
(Since cyclists cannot ride most trails in the national parks)
I much prefer the Yellowhead - Hwy 16, over the TCH - Hwy 1, or Hwy 93 - the old TCH.
From Jasper you can follow the old road to Athabasca Falls.
Make sure to take the fire road into the backcountry at Sunwapta Falls.
You can miss the TCH altogether by cutting east at Saskatchewan River Crossing.
Take Hwy 11 to Rocky Mtn House and Red Deer.
Then continue on Hwy 12 to the Saskachewan border.
Then follow Hwy 51 and Hwy 14 into Saskatoon - a college town.
From Saskatoon, you can head north of the Yellowhead Hwy on provincial roads -
Then cross north of Lake Manitoba and skirt north of Winnipeg to the Ontario border,
From there - unless you have a canoe - you have to get on the TCH.
I'll let someone with eastern experience continue in Ontario.