Yes it is possible for God to increase our intelligence. First of all, nothing is impossible for God. Lets look at Solomon as an example. Before we do that, what does Webster have for a definition of intelligence.
a (1) : the ability to learn or understand or to deal with new or trying situations :
reason;
also : the skilled use of reason
(2) : the ability to apply knowledge to manipulate one's environment or to think abstractly as measured by objective criteria (as tests)
Ok, Solomon. In 2 Chronicles 1:10, God asked Solomon,
"Ask what I shall give you." Solomon's response (which I love and have repeated his statement to God a number of times whenever I got called to pastor another Church) was
"Give me now wisdom and knowledge." Notice God's response in verse 11.
"God said to Solomon, "wisdom and knowledge are granted to you."
Lets look close at this event. You asked "Is it possible for God to increase our intelligence?" Webster says, "the ability to learn or understand." "Funk & Wagnalls" gives the definition of intelligence as, The quality of knowledge; ability to exercise the higher mental functions. Also, information acquired or communicated. Please notice that God told Solomon that wisdom and knowledge "
are granted to you." That tells me the answer to your question is yes.
It is my opinion, the preceding information is adequate to show that God can,
and does, increase one's intelligence. Thanks for the question.