How fast does activity affect synaptogenesis?
Synaptogenesis at such a fine temporal resolution is currently still best studied in animal models and reduced preparations where the activity levels can be more precisely controlled and advanced imaging methods can be used to monitor morphological changes. A series of studies with relatively high temporal and spatial resolution have been carried out in vitro and in vivo with two-photon microscopy on dendritic spines, which are considered as a proxy for the existence of synapses, since ~98% of them contain one.

The fastest effect after stimulation is the enlargement of pre-existing  or newly-formed spines and their synapses, as fast as ~2 min (Matsuzaki et al. 2004, Harvey et al. 2007, Hill and Zito 2013). Next, immature structures (often called filopodia) are starting to form within the first ~15 min (Maletic-Savatic et al. 1999). It is not yet clear what percentage of those structures bear an actual synapse, however they certainly have the potential to obtain one. A more gradual increase in the number of spines that persist for several hours and are very likely to contain a synapse occurs in later stages, ~30 min after stimulation (Engert and Bonhoeffer, 1999; Nägerl et al., 2004, 2007). However, note that the overall spine density is almost never affected in vivo (Holtmaat and Svoboda 2009), which indicates that compensating mechanisms counter-balance any synaptogenesis, so you should not expect to see an overall increased number of synapses.


References
- Matsuzaki, M., Honkura, N., Ellis-Davies, G. C. R., &amp; Kasai, H. (2004). Structural basis of long-term potentiation in single dendritic spines. Nature, 429(6993), 761–766. https://doi.org/10.1038/nature02617
- Harvey, C. D., &amp; Svoboda, K. (2007). Locally dynamic synaptic learning rules in pyramidal neuron dendrites. Nature, 450(7173), 1195–1200. https://doi.org/10.1038/nature06416
- Hill, T. C., &amp; Zito, K. (2013). LTP-Induced Long-Term Stabilization of Individual Nascent Dendritic Spines. Journal of Neuroscience, 33(2), 678–686. https://doi.org/10.1523/JNEUROSCI.1404-12.2013
- Maletic-Savatic, M., Malinow, R., &amp; Svoboda, K. (1999). Rapid dendritic morphogenesis in CA1 hippocampal dendrites induced by synaptic activity. Science (New York, N.Y.), 283(5409), 1923–1927. https://doi.org/10.1126/science.283.5409.1923
- Engert, F., &amp; Bonhoeffer, T. (1999). Dendritic spine changes associated with hippocampal long-term synaptic plasticity. Nature, 399(6731), 66–70. https://doi.org/10.1038/19978
- Nägerl, U. V., Eberhorn, N., Cambridge, S. B., &amp; Bonhoeffer, T. (2004). Bidirectional Activity-Dependent Morphological Plasticity in Hippocampal Neurons. Neuron, 44(5), 759–767. https://doi.org/10.1016/j.neuron.2004.11.016
- Nagerl, U. V., Kostinger, G., Anderson, J. C., Martin, K. A. C., &amp; Bonhoeffer, T. (2007). Protracted Synaptogenesis after Activity-Dependent Spinogenesis in Hippocampal Neurons. Journal of Neuroscience, 27(30), 8149–8156. https://doi.org/10.1523/JNEUROSCI.0511-07.2007
- Holtmaat, A., &amp; Svoboda, K. (2009). Experience-dependent structural synaptic plasticity in the mammalian brain. Nature Reviews Neuroscience, 10(9), 647–658. https://doi.org/10.1038/nrn2699