"Make meaningful progress" or "achieve significant progress" is a common way to express "取得有效进展" in Engpsh.

Examples:

"We have been working hard to make meaningful progress in our research project."
"我们一直在努力取得研究项目中的有效进展。"

"The company has achieved significant progress in its efforts to reduce waste."
"公司在减少浪费方面取得了显著进展。"

This phrase comes from the general usage of the word "progress," which means "forward or onward movement towards a destination." "Meaningful" and "significant" are added to emphasize that the progress made is notable and substantial.