Can we understand God in this life?

It depends:

A. No, with just the spirit of man in him, mankind only knows the things of a man (1Co.2:11). God is a mystery to those who are "of the spirit of the world" (1Co.2:12). The "natural man receiveth not the things of the Spirit of God... neither can he know them" (1Co.2:14.). Children only know "in part" (1Co.13:11.). It is the Gentiles who walk in the vanity of their mind, having the understanding darkened, being alienated from the life of God through the ignorance that is in them, because of the blindness of their heart (Eph.4:17-18).

B. Yes, when God reveals his deep mysteries to those who desire to become disciplined of him. Jesus said, It is given unto you (disciples) to know the mysteries of the kingdom of heaven, but to them, it is not given (Mat.13:11). God revealed those deep mysteries to believers in the early church by his Spirit (1Co.2:10). The ministers of Christ were stewards of the mysteries of God (1Co.4:1). Paul said, "In understanding be men" (1Co.14:20). John said, "We know that the Son of God is come, and hath given us an understanding, that we may know him that is true, and we are in him that is true, even in his Son Jesus Christ. This is the true God, and eternal life" (1Jo.5:20). Jesus said, "And this is life eternal, that they might know thee (Father) the only true God, and Jesus Christ, whom thou hast sent" (Joh.17:3).

The following are a list of scriptures that confirm God's intention for mankind to understand Him, and New Testament writers actually fulfilling that plan:

Isa.28:9 Whom shall he teach knowledge? and whom shall he make to understand doctrine? them that are weaned from the milk, and drawn from the breasts.

Heb.5:13,14 For every one that useth milk is unskilful in the word of righteousness: for he is a babe. But strong meat belongeth to them that are of full age, even those who by reason of use have their senses exercised to discern both good and evil.

Jer.3:15 And I will give you pastors according to mine heart, which shall feed you with knowledge and understanding.

Dan.8:16 And I heard a man's voice between the banks of Ulai, which called, and said, Gabriel, make this man to understand the vision.

Eph.1:18 The eyes of your understanding being enlightened; that ye may know what is the hope of his calling, and what the riches of the glory of his inheritance in the saints,

Eph.3:9 And to make all men see (understand) what is the fellowship of the mystery, which from the beginning of the world hath been hid in God, who created all things by Jesus Christ:

Rom.1:20 For the invisible things of him from the creation of the world are clearly seen, being understood by the things that are made, even his eternal power and Godhead; so that they are without excuse:

Col.1:9 For this cause we also, since the day we heard it, do not cease to pray for you, and to desire that ye might be filled with the knowledge of his will in all wisdom and spiritual understanding;

Col.2:2 That their hearts might be comforted, being knit together in love, and unto all riches of the full assurance of understanding, to the acknowledgement of the mystery of God, and of the Father, and of Christ;

1Jo.3:2 Beloved, now are we the sons of God, and it doth not yet appear what we shall be: but we know that, when he shall appear, we shall be like him; for we shall see him as he is.

1Jo.4:16 And we have known and believed the love that God hath to us. God is love; and he that dwelleth in love dwelleth in God, and God in him.

1Jo.4:17 Herein is our love made perfect, that we may have boldness in the day of judgment: because as he is, so are we in this world.

Jer.9:23, 24 Thus saith the LORD, Let not the wise man glory in his wisdom, neither let the mighty man glory in his might, let not the rich man glory in his riches: But let him that glorieth glory in this, that he understandeth and knoweth me, that I am the LORD which exercise lovingkindness, judgment, and righteousness, in the earth: for in these things I delight, saith the LORD.