Pull the notice record early
The core fight is rarely whether the sidewalk was defective. It is whether the responsible party, public or private, had notice of the defect long enough before the injury to have corrected it. Prior 311 complaints, code enforcement records, permit histories, and photographs or satellite imagery showing how long the defect existed are all worth pursuing at intake.
Trace the street tree
Because tree roots are a frequent cause of sidewalk lifting, investigate who planted and maintains any adjacent street tree. Some municipalities retain responsibility for tree-caused defects even where they have shifted general sidewalk maintenance duty to owners, which can keep the city in the case despite the general shift.
Name both, then let discovery sort control
In most cases the adjacent owner and the city both belong in the complaint, at least until discovery clarifies which party had actual control over and notice of the defect. Dismissing a potential defendant too early can foreclose recovery if that party turns out to bear responsibility.