"progresses toward" is correct and usable in written English.
You can use it when referring to movement from one point to another, usually in a gradual manner. For example, "The journey progresses toward the summit of the mountain".
Early neuromuscular denervation triggers compensatory sprouting of motor axons, and ultimately, progresses toward disconnection from skeletal muscle.
We may thus be seeing the gradual build-up of the disk as the source progresses toward its next outburst.
New York will continue to be tested as the team progresses toward the end of the regular season.
"A Body of Water," directed in a straightforward fashion by Maria Mileaf, does not deepen as it progresses toward a solution to the mystery at its heart.
McEwan's most recent novel, "The Children Act," progresses toward a holiday recital of Mahler's "Kindertotenlieder" and the emotional release it provides.
As Huawei advances in AI and progresses toward its aim of becoming a "full stack" company, however, it may increasingly seem too powerful for many in the West.
In addition, most cases of anorexia are preceded by an episode of dieting that progresses toward severe food restriction and self-starvation.
His interest in Shireen, mildly creepy at first, grows less mild and more sinister as the film progresses toward its final crisis.
As Nigeria progresses toward a new democratization program, it is even more critical for the country leadership to find viable ways of dealing with the "oil problem".
It has begun to expand in diameter as it progresses toward a red-giant phase, which is the end stage of a sun-like star's lifetime.
Leaf growth is determinate; the tip matures first, and maturation then progresses toward the base, after which the leaf cells cease to grow and divide.
