Was there a big switchover from wooden toys to plastic ones in the 1960s and 70s?
Wooden toys were common but hardly universal back then. As in past eras, children's toys were made from a variety of materials. Since the 1950s, those materials included various types of plastic. Polished glass (very thick, durable, and resistant to chipping or flaking; e.g., toy marbles) and metal (especially steel; e.g., Tonka trucks, Radio Flyer wagons, jacks, and Matchbox cars) were also commonly used.
Toys made out of wood have never disappeared from the market. There have been many such toys that were popular and commonly available throughout the period in question (from the 1960s through the present).
The popularity of individual products such as toy product lines rises and falls over time, driven by consumer interest. Some toy lines have remained while others have lost favor. The particular material that they are made from is one consideration when shopping for a toy, but there are plenty of other factors that influence the buying decision.
The material used in the manufacturing of specific toys are decided by the makers, based on numerous factors. There may have been an increase in the number of toy products made out of plastic over time due to the development of new plastic materials with favorable characteristics and an increase in manufacturing capacity and availability of such materials.
But there wasn't some wholesale changeover for the entire industry. Toymakers have always made their products out of a variety of materials.