Why didn't early jetliners use turbofans?
Production turbofans just weren't available. Once they came on the market and were mass-produced, jetliners switched to them.

While turboprops did exist at the time, they were (and are) a turbine engine driving a propeller in place of a piston engine, a straightforward combo of two techs. Turbojet engines were fairly complex machines for the era on their own. 

A turbofan involves a large diameter fan, similar in design to an axial compressor, which is more difficult to build than simpler centrifugal compressors used in the first jets and most turboprops. It spins at higher rpm than a prop, and needs to be built and balanced to jet engine tolerances, with the fan tips very close to the casing, but not quite touching it.

The fan also needs to be driven by a core that has enough net power left to produce both thrust and torque, and to do so at low enough rpm to keep the fan (mostly) subsonic. This combination only brings considerable efficiency gains with a two-spool core, using a low-speed shaft to match the fan's optimum rpm, fitted inside a hollow high-speed shaft driving the compressor (unless an aft fan is used). A two-spool with its extra seals is a much more complex engine than a single-spool turbojet or centrifugal flow turboprop. 

All of this was done and turbofans quickly became the norm, but it took a few years to develop and ramp up production.