Can G-d read our minds?

Question

In Devarim 8:2 it is written G-d test us in order to know what is in our hearts, so G-d uses an non-direct way to know what is in our hearts. Can G-d read our minds?

Answer 1

Yes Hashem can and does. This question is particularly appropriate for this time of year.

On Yom Kippur when we recite the vidui - confession section we say the following:

אתה יודע רזי עולם. . . ובוחן כליות ולב. אין דבר נעלם ממך

You know the secrets of the world...and probe his mind and heart, nothing is hidden from You.

In fact when looking in the Tanya, in Likkutei Amarim 41 it writes:

והנה ה' נצב עליו, ומלוא כל הארץ כבודו, ומביט עליו ובוחן כליות ולב אם עובדו כראוי. ועל כן צריך לעבוד לפניו באימה וביראה כעומד לפני המלך.

"And, behold, G‑d stands over him," and "The whole world is full of His glory," and He looks upon him and "Probes his mind and heart" [to see] if he is serving Him as is proper. Therefore he must serve before Him with awe and fear like one standing before the king.

In the explanatory section at the back of the Artscroll Yom Kippur Machzor (p.854) the introductory text to the section quoted above perhaps best encapsulates this concept:

We now acknowledge that G-d knows not only all that we have done, but all that motivated us to act as we did. He knows what we do privately, what we lust for, and how we rationalize our deeds. He knows the contradictions between our private and public behavior, and the personal preferences that influence our logic.

A similar choice of wording can be found in Yirmiyahu 17:10 where it writes:

אֲנִ֧י ה' חֹקֵ֥ר לֵ֖ב בֹּחֵ֣ן כְּלָי֑וֹת וְלָתֵ֤ת לְאִישׁ֙ כִּדְרָכָ֔ו כִּפְרִ֖י מַעֲלָלָֽיו׃ {ס}        

I the LORD probe the heart, Search the mind— To repay every man according to his ways, With the proper fruit of his deeds. (Sefaria translation)

The Metzudas Dovid there provides a similar explanation:

אני ה׳. ר״ל אולם אני ה׳ חוקר לב האדם ובוחן מחשבת הכליות לדעת מה הוא למען לתת לכל איש כדרכי לבו וכפרי מעלליו הם המחשבות שהם מעשה הלב ודרכיו

I Hashem - This means however, that I, the Lord, study the human heart and examine the thought of the kidneys¹ to know what it is to give to every man according to the ways of his heart. 'With the proper fruit of his deeds' are the thoughts that are the work of the heart and his ways

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¹ Refer to Gemara Brachos 61a where it writes that the kidneys are where the thoughts of man are formulated and similarly see Radak on the verse.

Answer 2

If the question is meant as was understood by @TamirEvan (in the comments) then the Sforno on that passuk provides an answer

לדעת את אשר בלבבך שיהי' מה שבלבך יוצא לפועל כדי שידע כל מלאך שבדין תהיה מעלתך יותר מן מלאכי השרת ותהי' עליך ידיעתי הפועלת לטוב כראוי לנמצא בפועל: לדעת את אשר בלבבך,

so that what you had in your mind will come to light, so that every angel will know that you had a justified claim to a higher rank in the universe than even the ministering angels.

So while G-D knows what’s in every persons mind, he specifically wanted it to be shown in the physical world so that the angels would know as well.