For some reason, the first line of my design doesn't start at the top but leaves a small space between top margin and first word. The paragraph style is:
Align to baseline grid
And the Grid increment setting is
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You probably have the wrong First Baseline Offset setting for this situation.
Select the text frame and open Text Frame Options using Cmd + B / Ctrl + B.
Switch to the Baseline Options tab:
The First Baseline > Offset specifies the vertical position of the first baseline of the text frame. You probably have it set to Ascent which is the default value. As you see there are five possibilities:
Ascent, Cap Height and x Height uses info found in the font file. Leading uses the leading of the text. Fixed allows for any custom position on or below the top edge of the frame.
In your case, to allow the text to start closer to the top edge, you should try Cap Height or x Height depending on what exactly you are trying to achieve.