Regarding chance of being hired into those roles without previous experience, I'd say they are minimal, unless you join a scrappy, low-wage startup (or other low-pay environment - perhaps government, academia?). Everybody else can afford to hire people with experience, and will likely choose them over you.

Instead, the way to laterally move into those positions is to work somewhere as a developer and express interest in moving into the desired position. There, you (hopefully) already have a product and org knowledge that is an asset over hires from outside company. Also, before the transition, you can just pick up some work that belongs to the target field, so people will over time see you as the "X" guy and the move will be very natural.

BTW Data Engineer is basically IC Programmer.