First Episode - Excellent
This is a cinematic level of excellence. Many modern TV shows are well-written, but I can't think of very many that have had the scope of Monarch. It's clear that a lot of thought, time, and effort went into crafting this. From the opening sequence of John Goodman fleeing from a giant monster to the horrifying final scene, this is top-notch television.
I appreciate that the creators are taking advantage of the extended format offered by a television show to build a compelling story. In lesser hands this would be nothing but an episode-by-episode kaiju battle, with each week being little more than a question of which monsters will show up for the requisite battle this time around. Instead, characters are being introduced and fleshed out, mysteries and puzzles laid out, and, best of all, a palpable sense of tension grows with each passing scene.
I also admire them for not dumbing things down for their audience. Instead of plastering "We're now back at the Tokyo apartment in 2015" on the screen, they simply shift from one scene to the next, and allow the key ring to appear in shot as the camera moves to someone sitting on a couch. Perhaps the more dimwitted viewer will lose track, but that's why god made the rewind button.
I'm about to dive into the second episode. They gave us two to open the series, with one per week to follow, and hope it continue at the level of the opener.