If you make headway, you progress towards achieving something.
make headway phrase oft with brd-neg, V inflects
There was concern in the city that police were making little headway in the investigation.
Translation English Cobuild Collins Dictionary
1 advance, improvement, progress, progression, way
2 make headway advance, come or get on, cover ground, develop, gain, gain ground, make inroads (into), make strides, progress
English Collins Dictionary - English synonyms & Thesaurus
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