By design, the only way to pause the game is using the escape key, which brings up the main menu on top of the stage you're currently playing. This is pretty standard puzzle game behavior, since being able to stop time would be a pretty big exploit in any action-oriented puzzle game (like how modern Tetris games are pretty broken by the fact that the Tetris Company demands that games allow the player to rotate a block indefinitely, giving players as much time as they want to think about a move even at the most difficult, high-speed levels).
That said, perhaps there are some things we can do to help make it easier for you to find combos. I suggest making good use of the right-click dimming feature, where right clicking on a block causes blocks of other colors to dim. This makes it very easy to see relevant blocks, and thus much easier to set up a chain. You can do the same with blocks that will fall as a result of that combo, right clicking on them to limit your view only to relevant blocks. If your goal is deep combos, I suggest trying to keep your chains small; the larger they are, the harder it is to keep track of the future state of the board and, thus, the harder it is to set up subsequent chains in the combo.
The most important part of getting deep combos, in my opinion, involves a method that is completely at odds with the intuitive method of planning everything in advance. Planning things in advance is good, but the deeper things go, the harder it is to keep it all in your head. You'll need to plan in advance in the actionless brainteaser mode, but in action modes, you want to only plan out two or three chains at a time and then look for new chains on the fly. In the amount of time it takes for one chain to complete, you should be able to find another chain to include in your combo. If you are fast enough and keep a good supply of blocks flowing by using the fast-forward feature, you can keep a combo going indefinitely, which is how I managed the scores I have on the Steam leaderboards.
So using the dimming feature is a huge help for finding potential chains to include in a combo, and adding chains to combos on the fly rather than planning it all out in advance is a necessity for getting around the inherent difficulty of a board with such spatial and temporal complexity. If you've played any of the Panel de Pon games (Tetris Attack, Pokemon Puzzle League, Planet Puzzle League), that same sort of mindset works very well here.
Also, a big help for doing things at a really fast pace is the Smart Drag feature that you can enable in settings. Smart drag lets you set up a chain with a single mouse drag by not letting you change the direction of blocks you've already dragged over until the next time you right click. This is fantastic for making chains that loop back over earlier blocks in the chain.
If you have any more questions about the game or its strategies, please don't hesitate to ask. I'm happy to try to help!