idioms - Where did Shakespeare get milk of human kindness from?

In Shakespeare's 1606 play "Macbeth" the titular character is filled with ambition to become king. His wife, Lady Macbeth, says to him:

Yet do I fear thy nature; it is too full o' the milk of human kindness to catch the nearest way

She used this phrase to say to her husband is not ruthless enough to achieve his ambitions. The phrase generally has come to mean compassion and/or care for others, maybe mercifulness or something similar. All the sources I've seen simply say this is the meaning of "milk of human kindness", and that it's from Shakespeare's play Macbeth:

Fig. natural kindness and sympathy shown to others. (From Shakespeare's play Macbeth, I. v.)
McGraw-Hill Dictionary of American Idioms and Phrasal Verbs

This phrase comes from Macbeth. In Lady Macbeth's soliloquy on the subject of her husband's character, she remarks... (what I quoted above)
Farlex Partner Idioms Dictionary

In the internet search I did the only information I could find is what the phrase means and that it came from Shakespeare's play Macbeth.

I'm wondering if anyone knows what the milk is for in "milk of human kindness". Was Shakespeare the first to use it? I've checked dictionaries and "milk" doesn't have any special meanings I'm not aware of. The closest connection I can make is that milk is fed to a mother's young, and that that act can be seen as an act of self-sacrifice, love, maybe compassion in providing the nourishment for her little ones. Still, people are said to "have the milk of human kindness"; is "milk" here some metonym for love or sympathy or compassion?