Assuming that the "400 silent years" are legitimately (and approximately) 400 silent years prophetically (and I understand there are many who do not), could there be a parallel to the 400 (430) years in Egypt, when it seemed that God was silent with His people?
I think we have to look carefully at the years in "Egypt" before jumping to conclusions about what they were and whether God was actually "silent" with His people during this time.
If you find a Bible map that shows "Egypt at its zenith," you will note that during the time when Abram entered "Canaan" it was all part of "Egypt." In other words, Abram/Abraham sojourned in Egypt as soon as he had left Haran (after his earlier departure from Ur of the Chaldees--see Genesis 12). It was also Canaan, but was not independent of Egypt until nearer the time of Jacob or Joseph.
During Abraham's time in "Egypt" (Canaan), he also fathered a son with an Egyptian (Hagar). It was this son, later seen bullying the promised child of Sarah, that prophetically started the "400 years" in Egypt.
And he said unto Abram, Know of a surety that thy seed shall be a stranger in a land that is not theirs, and shall serve them; and they shall afflict them four hundred years; (Genesis 15:13, KJV)
The prophecy does not say for how many years the Israelites would be slaves; it says only that they would be afflicted for four hundred years, and that they would "serve" (implying slavery). The "afflict" portion of this prophecy came with Ishmael's affliction of Isaac.
The Full Count of Years
40 Now the sojourning of the children of Israel, who dwelt in Egypt, was four hundred and thirty years. 41 And it came to pass at the end of the four hundred and thirty years, even the selfsame day it came to pass, that all the hosts of the LORD went out from the land of Egypt. (Exodus 12:40-41, KJV)
Now, let's subdivide that.
So Abram departed, as the LORD had spoken unto him; and Lot went with him: and Abram was seventy and five years old when he departed out of Haran. (Genesis 12:4, KJV)
Abraham was 75 when he left Haran. This is the same year he entered Egypt (Canaan).
And Sarai Abram's wife took Hagar her maid the Egyptian, after Abram had dwelt ten years in the land of Canaan, and gave her to her husband Abram to be his wife. (Genesis 16:3, KJV) And Abram was fourscore and six years old, when Hagar bare Ishmael to Abram. (Genesis 16:16, KJV)
Abraham was 86 when Ishmael, the son of the Egyptian, was born.
And Abraham was an hundred years old, when his son Isaac was born unto him. (Genesis 21:5, KJV)
Abraham was 100 when Isaac was born.
8 And the child grew, and was weaned: and Abraham made a great feast the same day that Isaac was weaned. 9 And Sarah saw the son of Hagar the Egyptian, which she had borne unto Abraham, mocking.(Genesis 21:8-9, KJV)
At this point we make an educated assumption, knowing the details of the prophecy and the customs of the time, that this weaning occurred when Isaac was five years old. Ishmael would have been 14 when Isaac was born, and by this time he is nearly a man at age 19 when he mocks the child.
The 430 years' time of the sojourn in Egypt began when Abram was 75. The 400 years' of affliction, and later bondage, began when Abraham was 105, and Isaac was five. During the 30 intervening years, Abraham may have been afflicted, but it was not his promised seed who was afflicted, as would fulfill the prophecy.
From the time of Isaac (who lived 180 years, 60 years to birth of Jacob; Gen. 35:28; Gen. 25:26), to Jacob (147 years, 130 year to entry into "Egypt" proper with household--Joseph then being about 39 years old; Gen. 47:28; Gen. 47:9; Gen. 45:6; Gen. 41:46), to Joseph (110 years; Gen. 50:22), and beyond Joseph's death to the time of the forced slavery was quite a number of years. As we do not know the exact year past Joseph's death in which the bondage began, we can only estimate this period of time at somewhere between 90 and 120 years.
From the start of the 400-year prophecy, when Isaac is 5, to the point where Joseph dies, is about 256 years (55 years of Isaac to birth of Jacob, plus 130 years of Jacob to his "entry" into "Egypt"--no longer in its zenith--at which time Joseph is 39, plus 71 remaining years for Joseph). At least a few years are expected to have passed following Joseph's death before his memory and honor, having saved Egypt from the famine, would have been forgotten, and the slavery could begin.
Many assume that the period of slavery was a full 400 years. But this is not accurate in the least. It was far less than four centuries of actual bondage. The affliction began early, and started the prophecy, but the bondage was, mercifully, a much shorter period.
Was God "silent" during those 400 years?
No. The birthright blessings given by Isaac to Jacob, by Jacob to his twelve sons, and even by Joseph before he died, contained inspired prophecies that applied to the Israelites well into the future.
Was God "silent" during those ~90-120 years of actual slavery in Egypt?
No. It was during those years that Moses, who had escaped Egypt, wrote the books of Job and Genesis while out tending the sheep of his father-in-law Jethro. We know also that Moses heard God's words at the burning bush while the Israelites were still enslaved in Egypt.
There was no period of 400 years of silence in Egypt. While there was a 400-year period of silence before Christ, there is no clear parallel to the 400/430 of Egypt.