There are upper_case and lower_case commands:
{ "keys": ["ctrl+k", "ctrl+u"], "command": "upper_case" },
{ "keys": ["ctrl+k", "ctrl+l"], "command": "lower_case" },
I'm searching for command to capitalize the first letter of string, which can be assigned to custom shortcut.

Under
Edit -> Convert Caseis theTitle Caseoption. The following key binding should work:Add this to your custom keymap, and it will override the default command for CtrlK,CtrlT -
fold_tag_attributes. Alternatively, you can usewhich is not assigned to anything in the default Sublime keymap.
If you're interested in other types of conversions, check out the
Case Conversionplugin on Package Control. It installs commands forsnake_case,camelCase,PascalCase,dot.case, anddash-case, along with a few other utilities, such as a function to separate words with slashes.