Here are some key passages that reference some of God’s traits that clearly have a maternal feel to them:
Isaiah 66:13
For thus says the Lord:
       “Behold, I will extend peace to her like a river, and the glory of the nations like an overflowing stream; and you shall nurse, you shall be carried upon her hip, and bounced upon her knees.  As one whom his mother comforts, so I will comfort you;
 
Isaiah 49:15
Can a woman forget her nursing child, that she should have no compassion on the son of her womb? Even these may forget, yet I will not forget you. Behold, I have engraved you on the palms of my hands;
When I was young, we raised birds. One of the things that some mother birds do, like turkeys for example, is to protect their young by covering them with their wings. They do this in storms, in particular. It is a particularly maternal thing. God refers to Himself in these:
Deuteronomy 32:11 (as well as Ps 17:8, Ps 57:1, Ps 91:4)
Like an eagle that stirs up its nest, that flutters over its young, spreading out its wings, catching them, bearing them on its pinions, the Lord alone guided him,
 
Luke 13:34, Jesus puts Himself in that same role, too.

 
O Jerusalem, Jerusalem, the city that kills the prophets
 
and stones those who are sent to it! How often would I have gathered your children together as a hen gathers her brood under her wings, and you were not willing!
 
or perhaps a more ferocious animal?
Hosea 13:8
I will fall upon them like a bear robbed of her cubs;
I will tear open their breast,
       and there I will devour them like a lion,
as a wild beast would rip them open.
Luke 15:8-10, Jesus tells a parable in which the God-figure is a woman:
Or what woman, having ten silver coins, if she loses one coin, does not light a lamp and sweep the house and seek diligently until she finds it? ⁹ And when she has found it, she calls together her friends and neighbors, saying, ‘Rejoice with me, for I have found the coin that I had lost.’ ¹⁰ Just so, I tell you, there is joy before the angels of God over one sinner who repents.”
Ps 22:9-10, Ps 71:6, and Isa 66:9 all put God in the role of a midwife. Though it says “he”, the midwife in Israel was apparently a female role.
Yet you are he who took me from the womb;
you made me trust you at my mother’s breasts.
 Upon you I have leaned from before my birth;
you are he who took me from my mother’s womb.
 My praise is continually of you.
Bless our God, O peoples;
let the sound of his praise be heard,
who has kept our soul among the living
and has not let our feet slip.
 Shall I bring to the point of birth and not cause to bring forth?”
says the Lord; “shall I, who cause to bring forth, shut the womb?” says your God.
Our concepts of gender, though cultural and society, are connected to sex – which is biological. Honestly, we cannot know what role gender or sex will play in the new imperishable bodies that humans will have someday forever. Much less, the role of gender in God – but how could what we know as sex have anything to do with a self-existent Spirit being as God is with no need of sex or biological reproduction?
So, it is completely error to think that God being “He” somehow is a tipped hat to human sex or gender except as being in language that we would understand. God has reveled Himself somehow as “He” and therefore that is the correct pronoun for Him, but be

very careful about ascribing any meaning there – it is very easy to make big mistakes.
Remember that God so loved the world – all men and women – perhaps all of creation – that He sent His Son. God’s love extends to everyone and whether you are male or female, He treasures you.