Hey Tommy,
You don't have to look for the note (see “show newNote)”:
tell application "Notes"
activate
set newNote to make new note
show newNote
end tell
The problem with this is that AppleScript does NOT position user-focus in the note, so you can get on with editing...
You're better off using plain old Keyboard Maestro actions:
Make New Note v1.00.kmmacros (6.5 KB)

You can do this with AppleScript, but the behavior of the new note is a bit different. Normally a new note's first line is formatted in title-format, but when created with AppleScript it's body-format.
--------------------------------------------------------
# Auth: Christopher Stone
# dCre: 2021/08/05 03:43
# dMod: 2021/08/05 03:43
# Appl: Notes, System Events
# Task: Make a New Note and Focus for Editing
# Libs: None
# Osax: None
# Tags: @Applescript, @Script, @Notes, @System_Events, @Make, @New, @Note, @Focus
# Test: macOS 10.14.6 & Notes 4.6
--------------------------------------------------------
tell application "Notes"
activate
set newNote to make new note
show newNote
end tell
tell application "System Events"
tell application process "Notes"
tell window "Notes"
tell splitter group 1
tell splitter group 1
tell group 2
tell scroll area 1
tell text area 1
set focused to true
end tell
end tell
end tell
end tell
end tell
end tell
end tell
end tell
--------------------------------------------------------
-Chris