Hey!
The one key tip for intros in persuasive writing: Give the scenario context.
For example; if you were asked to write a letter to the headteacher about the litter problems within the school, you shouldn't start it
"I am writing to you to inform you of the litter issues within the school and what we can do to fix it"
Instead, give it context. The easiest context is either a survey or a school council meeting.
"I am writing to you following a recent survey held within the school, requesting students opinions regarding the school site. When posed the statement 'I would say the school site is clean and well-maintained' 78% of students either disagreed or strongly disagreed. I decided to study the school site myself after collecting these results, and was left appalled when" blahblahblah etc.
You never write a letter/make a speech/write an article for no reason. There will always be a purpose behind it. If you write that purpose into your introduction, it improves your response SO much.
Don't treat it as an exam, pretend you're actually performing the task in real life - would you write to someone for no reason? Something must have spurred you to write whatever it is that you have written.
Hope this helps! Good luck x