[mothered]

As informed, this package is considered delivered and received by its recipient

Given they've stated "received by Its recipient", tell them to provide photographic evidence of yourself personally accepting the package.

They just sent me a signature, probably the delivery man's, which does not belong to me at all.

Did you tell them It does not belong to you?

They said :
Thank you for contacting New Balance online customer service.

The term "escalate" is used in other customer services .

Nonsense.

This claim pertains to a customer service Issue, hence you have every right as a buyer to request an escalation.

Our procedures are clear and strict regarding delivery, and we have fulfilled our commitments

You don't have your goods, thus they did not fulfil their commitments.

There is no need to contact us again for this request neither by email nor by chat, as the customer service members as well as the hierarchy will give you the same answers already given.

Total BS.

Ask your claim be escalated and reviewed on a senior level.

If you need further assistance, please do not hesitate to contact me again.

Hilarious.

They've stated this:

There is no need to contact us again for this request neither by email nor by chat

But have concluded their message to contact them for assistance. Try and work that out?

I don't know what to do anymore

As per all the aforementioned details, I've given you all the tools and advice to effectively handle It.