When you go to a DTA/DHCD office to apply for EA, you should bring as many documents as you have that may help show you are eligible for EA. But if you need shelter right away, DHCD is not allowed to deny you shelter just because you do not have all the proof (verification) at the time you apply.
If you appear to be eligible based on your own statements and other information available to DHCD (such as information in the DTA and DHCD computer systems), DHCD must place you in shelter and give you 30 days to get necessary verifications. This is known either as "presumptive eligibility," or "presumptive placement" or "placement pending verifications". 760 CMR 67.06(1)(c). See also Housing Stabilization Notice 2012-08. If you need help getting verifications, your DHCD worker or the shelter provider should help you get them. 760 CMR 67.04(c).
DHCD says that the presumptive eligibility rules do not apply to documents that prove the identity, relationship, or Massachusetts residency, and that such documents must be provided before an eligibility determination and placement will be made. See Housing Stabilization Notice 2012-08. This is inconsistent with the statutory requirement of placement pending verifications. You should always try to provide as many verifications as you can at the time of application, but if you do not have needed verifications readily available and have no place safe to stay and DHCD refuses to place you due to lack of any verification, contact an advocate.