There is a lot of debate over what "thoughts" are in terms of consciousness, and this has been referred to as the "hard problem". However, it seems pretty clear that in some form patterns of brain activity are the "stuff" that underlies a thought/idea: if you change patterns of brain activity, you change the thought.
Therefore, I would describe a "new" idea as a "new pattern of brain activity" rather than connections. While the exact timescale of a "pattern" should be is unclear, perhaps a few hundred milliseconds is a good guess (see for example Luczak et al 2015, and the recent paper by Davis et al 2020). Brain activity is constantly shifting, of course, so really every moment experienced is a new thought of some sort.
There are too many studies to name all of them that show that some consistent pattern of brain activity is associated with some thought. The review by Harris, 2005 is a favorite of mine, but there are many levels of analysis to approach these questions. You might find some more compelling work among the studies of the biological basis of perception.
One particularly elegant paper is Liu et al, 2012. They used some molecular tricks to identify neurons in a rodent brain that are activated during a fearful context, and they cause long-term expression of a protein in those specific cells that they then use to reactivate those same cells at a later time. Reactivating those cells causes the fear behavior to return, effectively triggering the same ideas.
Connections between cells can also change pretty rapidly, but this would be better described as memory rather than an initial thought or idea. This can involve de novo creation of synapses, but more often is studied as a change in synaptic strength. Weak synapses can be strengthened with certain input patterns, and we call this long-term potentiation. The idea of connections between neurons as the stuff of memory goes back some 100 years to Ramón y Cajal.
Davis, Z. W., Muller, L., Martinez-Trujillo, J., Sejnowski, T., & Reynolds, J. H. (2020). Spontaneous travelling cortical waves gate perception in behaving primates. Nature, 1-5.
Harris, K. D. (2005). Neural signatures of cell assembly organization. Nature Reviews Neuroscience, 6(5), 399-407.
Liu, X., Ramirez, S., Pang, P. T., Puryear, C. B., Govindarajan, A., Deisseroth, K., & Tonegawa, S. (2012). Optogenetic stimulation of a hippocampal engram activates fear memory recall. Nature, 484(7394), 381-385.
Luczak, A., McNaughton, B. L., & Harris, K. D. (2015). Packet-based communication in the cortex. Nature Reviews Neuroscience, 16(12), 745-755.