Is it permissible to ponder the existence and attributes of God?

If the contemplation is about the how of Allah's existence and His essence, then it is impermissible, as it is a deception from Iblis. Abu Hurayrah reported that the Messenger of Allah, peace and blessings be upon him, said: "Satan comes to one of you and says, 'Who created this and that?' until he says to him, 'Who created your Lord?' When he reaches that point, let him seek refuge in Allah and desist."

As for contemplating Allah's creations that indicate His existence, it is permissible. Contemplating them guides the servant to His Oneness. Allah the Almighty said: "and they give thought to the creation of the heavens and the earth." Similarly, contemplating the meanings of Allah's names and internalizing them is permissible, so that the servant may increase in reverence and awe of Allah. Contemplation leads to good results in matters that can be comprehended. As for matters that cannot be comprehended, contemplating them is a waste of time and may lead to what is forbidden, such as contemplating the how of Allah's attributes. Contemplating the meanings of Allah's names is مطلوب (desired/required), as Imam Malik said: "The istiwa' (ascending) is not unknown, its kayf (how) is incomprehensible, belief in it is obligatory, and asking about it is an innovation."