Yes, it is possible to apply for a US trademark even if you don't have the specimens of use yet. You can file your application using the Intent to Use filing basis, which is reserved for applicants not using the mark in US commerce at the time of filing (as opposed to the Use in Commerce filing basis).
In this case, the USPTO will first complete the preliminary assessment of your application, which can take several months, depending on the current backlog at the USPTO. If everything is in order, your application will be published for oppositions for another month. If there are no unresolved oppositions or a request from a third party to extend this window, the USPTO will then request the specimens from you, giving you six months to file them with a Statement of Use.
This gives you several months to prepare your specimen. If you can't meet the deadline for the SoU submission, you can ask for a six-month extension. You can ask for five extensions, giving you a total of 36 months to provide the specimen, counting from the date the USPTO requests them from you.
