Just after their awakening, Men were able to communicate directly with Eru ("the Voice"), as illustrated in this tale present in Morgoth's Ring (part of Tolkien's unpublished drafts):
The Voice said: 'Ye are my children. I have sent you to dwell here. In time ye will inherit all this Earth, but first ye must be children and learn. Call on me and I shall hear; for I am watching over you.'
In that time we called often and the Voice answered. But it seldom answered our questions, saying only: 'First seek to find the answer for yourselves. For ye will have joy in the finding, and so grow from childhood and become wise. Do not seek to leave childhood before your time.'
This changes, however, once Morgoth's lies lead Men to abjure the Voice (calling it the manifestation of void and darkness):
The first Voice we never heard again, save once. In the stillness of the night It spoke, saying: 'Ye have abjured Me, but ye remain Mine. I gave you life. Now it shall be shortened, and each of you in a little while shall come to Me, to learn who is your Lord: the one ye worship, or I who made him.'
This is the original sin of Men alluded to in the Silmarillion, and the reason why Men tries hard to forget their past before arriving in Beleriand.