The Quran

وَيَقولونَ لَولا أُنزِلَ عَلَيهِ آيَةٌ مِن رَبِّهِ ۖ فَقُل إِنَّمَا الغَيبُ لِلَّهِ فَانتَظِروا إِنّي مَعَكُم مِنَ المُنتَظِرينَ

Muhammad Asad

NOW THEY [who deny the truth] are wont to ask, "Why has no miraculous sign ever been bestowed upon him from on high by his Sustainer?"¹ Say, then: "God's alone is the knowledge of that which is beyond the reach of human perception.² Wait, then, [until His will becomes manifest:] verily, I shall wait with you!"

I.e., on Muhammad, in order to "prove" that he is truly a bearer of God's message (a sceptical objection which resumes the theme enunciated in verses 1-2 and 15-17 above); see also 6:37 and 109 and the corresponding notes, especially note 94. The pronoun "they" refers to both categories of deniers of the truth spoken of in the preceding passages: the atheists or agnostics "who do not believe that they are destined to meet God", as well as those who, while believing in God, "ascribe a share in His divinity" to all manner of imaginary intercessors or mediators (see verse 18 above).
This answer relates not merely to the question as to why God has not bestowed on Muhammad a "miraculous sign" of his prophethood, but also to the "why" of his having been chosen for his prophetic mission. See in this connection 2:105 ("God singles out for His grace whom He wills") and 3:73-74 ("God is infinite, all-knowing, singling out for His grace whom He wills")