"Thy Kingdom Come" is ἐλθέτω ἡ βασιλεία σου and the verb can be translated, with the syntax used, as "emerge."
The whole context of Matt 6 is one of secrecy - where God's reign and influence are sneaking upon us. Interpreters often make the mistake of "will reward you" (vv 6:4&18)as something that awaits us above and beyond. I believe the rewards are expanding here and now.
Having my "sky-time" (bible & meditation) this morning - I realized a curious retrospective. Israel begs for a king. YHWH says they don't need one. They whine and like a loving parent a king is allowed (but with a lengthy "please be advised" disclaimer). They wanted a mere horizontal influence.
Then YHWH's people decide that a temple needs to be built. Again, God resists the notion. They persist and like a loving parent a temple is allowed (but with a lengthy "please be advised" disclaimer as well). They wanted a mere horizontal influence.
I read through the end of 2 Samuel and into 1 Kings (where David - "the man after God's own heart" releases his life-long bitter grudges and tells Solomon to "whack" a few guys he didn't like).
Solomon takes over and prospers big-time. He takes 7 years to build the temple and offers a very insightful prayer when it is dedicated. Then the narrative truncates his 13-year devotion to building his palace (something I don't recall ever being asked for and granted). I cringe knowing where all this will lead. I have read this story a few times before.
Within a handful of verses, Solomon finds himself being sucked down into a consequential vortex. All the peace and prosperity of his great horizontal influence turns out to be short-lived. Solomon dies and his son Rehoboam takes over.
The "kingdom" divides and many years of intermittent trouble and success follow.
Something that jumped off the pages (God's Word keeps doing that!) surprised me in the midst of the consequential conflicts and chaos. The words "this is my doing" made me realize the huge sovereignty God possesses.
1 Kings 12
22 But this word of God came to Shemaiah the man of God: 23 "Say to Rehoboam son of Solomon king of Judah, to the whole house of Judah and Benjamin, and to the rest of the people, 24 'This is what the LORD says: Do not go up to fight against your brothers, the Israelites. Go home, every one of you, for this is my doing.' " So they obeyed the word of the LORD and went home again, as the LORD had ordered.
Then I had one of those cinematic flashbacks of the history that followed (sounds strange putting it that way).
The kingdom goes awry and the temple is dashed to the ground. Then the temple gets rebuilt later and is dashed to the ground. Then the temple gets rebuilt later and is dashed to the ground.
Hmmm. It's still absent and there is no earthy monarchy where God's people have prevalence. Which returns me to the ideas that Jesus promoted in his lengthy discourse on a hillside.
Our influence was never intended to be exercised and experienced on a mere horizontal plane. Jesus advocates drawing on the invisible influence and reign of God to allow his pure dominance to flow through us to others - without calling attention to ourselves (that's one reason I don't where an advertising team T-shirt when I'm participating in a "mission project").
And the increment of this is a daily one. How often I overlook the "divine encounters" because I've got this idea that it will all happen in some venue that has yet to arrive in some type of form that would correlate to a king and a temple. I guess that's why I really went to seminary - so I could be the "pastor" of a "church" and then I could really accomplish so much more for God.
Such a journey continues. It's a very intriguing one. YHWH's Kingdom is continually emerging. There's nothing that should keep us waiting until something else happens or arrives.