I think it's avoidable to a certain extent. You can introduce her with the nickname you like and people will follow suit. Once she's in school though, she might want to switch it up! I'm in the same boat, I love a name but dislike the common nicknames so I will be introducing her with a nickname I enjoy to family and friends!
I know (of) two Matildas - one goes by Matty, the other Tilda. The one that goes by Matty uses her full name quite a bit though, while Tilda goes by Tilda almost exclusively. I think Tilly and Tilda are just as intuitive as Matty/Mattie, if not more, and Milly is a good option that isn't too much of a stretch either. It's definitely avoidable, but I think you'd need to choose an alternative nickname, so you can reinforce it before she starts school and other kids call her Matty. If they hear you saying "Bye, Tilly" in the playground in the morning they'll call her Tilly as a nickname, or whatever you choose to use.
I understand your pain it is awful to introduce yourself by your first name only to have that person immediately and without asking call you by a nickname. It urked me so much that I decided to use my middle name.
In your case I would introduce the baby as Matilda and make it known that her nn is Tilly and I would make a strong point of it to anyone who oversteps the mark and calls her Mattie, it is so annoying.
Matilda is a terrific name.
I really think that any nickname is avoidable if you want it to be. My sister's name is Mary Catherine...not M.C., not Mary, not Mary Kate...Mary Catherine. Every time someone called her something other than Mary Catherine she or a family member would correct them and eventually everyone who knew her knew what she wanted to be called.
I think if you want a little Matilda, then that is exactly what you will have. If someone calls her Mattie just say "we prefer Matilda" and I can't imagine anyone would go against your wishes.
If you introduce her as "Matilda" and people then call her "mattie" just correct them.
However, be warned that its possible your daughter herself might want to be called "Mattie". This may never happen. But if you honestly cannot stand even the thought that she might ask you one day to only call her Mattie...then perhaps the name isn't for you.
I live in the UK, where I live Matilda is used frequently and the only nickname used for the various of Matilda's I know is Tilly or Tilda. Mattie is never used as this nickname is associated with Matthew. Thus people do not associate the masculine choice of Mattie with Matilda unless it's thrust upon them. For example the child is introduced as Matilda but people call her Mattie. Otherwise all the Matilda's I know are Tilly or Tilda. Maybe it's different where your from but where I am that would be the natural nickname choice. Like Evie is the natural nickname for Evangeline and Angie is for Angelica.
My mind goes to Tillie first, actually. Tilda?
Mattie wouldn't pop up for me I think because of Maddie via Madeleine/Madelyn/etc.
ETA: I think my brain goes to the stressed syllable for nicknames. I say Matilda muh-TILL-duh, so the "til" pops out as the nickname source. This vs. MAD-uh-lin which shortens to Maddie.
Funny, I've had this same thought when we were considering Matilda. I love Matilda and anything in the Tillie, Tilda, Tildie vein, but really dislike Mattie. Also don't like that it lumps it into the Madison/Madeline/etc group.
Glad to hear that many think avoiding Mattie is definitely possible!