This requires a bit of a history lesson. 
In 2005, researchers noted that most intercity car journeys follow a similar pattern. Broadly speaking, you take a residential road from your house onto a distributor road; then you follow that distributor road to a main road; then you follow that main road to a motorway; you do most of the miles on that motorway; then you turn off onto a main road, then onto a distributor road, then onto a residential road which takes you to your destination.
Essentially, highway systems are ordered according to a hierarchy, and most long-distance journeys simply navigate up that hierarchy and down again. A router can exploit this to find an A–B route quickly. Rather than exploring every single turn along the way, they trust in the roads higher up the hierarchy to return results more quickly. This algorithm is called Highway Hierarchies.
The signposted highway system is usually the fastest way by car from one place to another, but not always. Not all routing applications have signposted hierarchical highway systems (e.g. walking and sometimes cycling). So what if we could devine our own hierarchy?
That is what the followup algorithm does, Contraction Hierarchies (2008) - still one of the core algorithms used by route-planners today. Essentially, this constructs a hierarchy by looking at the speeds/distances on each road, rather than just trusting in the official classification. It might find, for example, that the best driving route from Gloucester to Ross-on-Wye is A40->B4215->B4221->M50->A40, even though that requires descending the formal hierarchy (A40->B4215) and then ascending it again.
It then records that route in its internal hierarchy as “best route between Gloucester and Monmouth”. As it builds the hierarchy upwards, that route may in turn form part of “best route between Oxford and Newport”. And so on.
In other words, route-planners have already worked out a network of the best continuous cycle routes between any two points. That’s how cycle.travel and other sites are able to find you the best route from Brussels to Rome in under a second - they use their computed hierarchy. It doesn’t matter whether there are gaps in the formal cycling infrastructure: the route-planner will find its way. If you want to show a network but there’s no on-the-ground evidence that you can map in OSM, this, I think, would be the place to start.