This is a good example of not seeing the forest for the trees. Or, in this case, seeing the context for the grammatical details. Paul, when he writes of "lower places of the Earth", is actually drawing upon several OT passages, notably Isa. 44:21-23:
“Remember these, O Jacob,
And Israel, for you are My servant;
I have formed you, you are My servant;
O Israel, you will not be forgotten by Me!
I have blotted out, like a thick cloud, your transgressions,
And like a cloud, your sins.
Return to Me, for I have redeemed you.”
Sing, O heavens, for the LORD has done it!
Shout, you lower parts of the earth;
Break forth into singing, you mountains,
O forest, and every tree in it!
For the LORD has redeemed Jacob,
And glorified Himself in Israel.
Notice especially the parts underlined. The "lower parts of the earth" are contrasted to the "heavens". These "lower parts" are simply lower in comparison to the heavens. The whole passage is from God's point of view, and is a praise that God - Christ - would go "slumming" - leave His majesty and come down to where we live, the lower parts - to rescue us.
Notice also that these lower parts have mountains and trees. This is just the earth. Other verses can also be drawn upon but this should be enough.
The whole Jude 6 passage is another misconstruction on what the Bible actually states. People like Chuck Missler have really muddied the water on this passage by their sensationalistic slant on Jude (and Gen 6.) But that would be another thread altogether.
so shall the Son of man be three days and three nights in the heart of the earth. Would you say the heart of the earth and the lowest parts of the earth
could be the same?
and are the children of God, being the children of the resurrection. Does this imply birth from the earth?
the firstborn from the dead; Does this imply birth from the earth?
Isa. 66:8 Who hath heard such a thing? who hath seen such things? Shall the earth be made to bring forth in one day? [or] shall a nation be born at once? for as soon as Zion travailed, she brought forth her children. Does this imply birth from the earth?
Isa 26:19 Thy dead [men] shall live, [together with] my dead body shall they arise. Awake and sing, ye that dwell in dust: for thy dew [is as] the dew of herbs, and the earth shall cast out the dead. Is birth from the earth not implied here?
In Isa. 66 it is Zion giving birth also. Where is Zion when she gives birth?
I will build my church;(
Zion) and the gates of hell shall not prevail against it. (Because in one day she shall give birth to the kingdom of God because death the gate in to hell shall not prevail over her just as it could not of her head Christ. Acts 2:24 Whom God hath raised up, having loosed the (Birth) pains of death (Should have said hell) because it was not possible that he should be holden of it.
And last but not least Psalm 139:14-16 I will praise thee; for I am fearfully [and] wonderfully made: marvellous [are] thy works; and [that] my soul knoweth right well. (Where was it resurrected from) My substance was not hid from thee, when I was made in secret, [and]
curiously wrought in the lowest parts of the earth. Thine eyes did see my substance, yet being unperfect; and in thy book all [my members] were written, [which] in continuance were fashioned, when [as yet there was] none of them.
This was speaking of the dead Jesus the Christ and his members the church.
Compare with Hebrews 5:7-9 Who in the days of his flesh, when he had offered up prayers and supplications with strong crying and tears unto him that was able to save him from death, and was heard in that he feared; Though he were a Son, yet learned he obedience by the things which he suffered;
And being made perfect,
he became the author of eternal salvation unto all them that obey him;
But made himself of no reputation, and took upon him the form of a servant,
and was made in the likeness of men: