There are a few techniques that I've tried myself which have been effective for scaling combat challenges up or down, and they should apply to series of encounters just as well.
1. Adjust the number of enemies in combat
The action economy is a big deal, especially when enemy groups mix types of enemy to allow more possible combinations of actions the enemy party can take per round. This is often the case in ToD, especially the early sections where players will be dealing with kobolds and dragon cultists.
Adding more enemies means a greater total amount of enemy HP they have to reduce, more damage-dealing actions need to be taken, and more attacks/battlefield control maneuvers that the players will need to deal with. I've found that adding more enemies tends to make combat more difficult.
2. Adjust the stats of enemies in combat
This one has a lot of variety available. Increasing HP is the easiest and most straightforward change to adjust combat in a predictable way. I've found that increasing enemy HP makes combat take longer, which may or may not meaningfully change its difficulty. I've also found that adjusting HP to make one-shot kills harder for the players to achieve makes combat feel not-easy (it isn't necessarily hard, but each player blowing away 1+ enemies with each attack/round feels particularly easy).
Changing enemy equipment can make a big difference. Swapping daggers for longswords means higher-damage dice facing the players on each attack. Giving magic items has an even bigger effect, but may not be necessary/congruent with the plot, and potentially gives players access to those items as loot after combat. I prefer to avoid this (magic items can be impactful), so I do not favor giving enemies magic items for balancing, in general. But it's not hard to compute hit probabilities of different weapons against your players' AC, which you'll already know.
Changing other stats can have subtler effects which are harder to predict and can change the experience of combat a lot, and so I strongly encourage reviewing some data using AnyDice or gaming out changes yourself with mock combat encounters while you plan. Increasing AC can really add a lot to an enemy's survivability, but can also make players frustrated at being able to hit only rarely.
3. Adjust the composition of enemies in combat
ToD has a lot of kobolds and cultists, but you don't have to use those. Swapping non-caster cultist stat blocks for, say, Veteran stat blocks makes for a deadlier opponent. And who's to say that the cult can't recruit some more capable members? You can bring in Winged Kobolds (or other variants) rather than using the standard kind. Or total different enemies! The cult has a lot of resources behind it, and could certainly recruit/train/otherwise acquire deadlier resources with which to threaten the players.
4. Adjust enemy tactics in combat
I really like this option, but it requires some familiarity with the combat system and the characters involved, plus some practical evaluation (as above, I like mock-combats, but other approaches exist too). Enemies can be stupid and uncoordinated, beelining to the nearest PC and attacking until one of them goes down. Or they can be highly tactical, exploiting terrain features, special abilities, PC/party weaknesses.
Kobolds and cultists give you some nice options in this regard. Kobolds get Pack Tactics, which gives them advantage on attacks when they're in close proximity around an opponent. Bad kobold tactics involve sparsely arranged kobolds attacking individually. Good kobold tactics involve surrounding and mobbing opponents, with Advantage on each attack. Some cultists are spellcasters (and it can be all of them, if you're trying to make things more challenging), which means they have options for controlling the battlefield in various ways that enhance the kobolds' mobbing.
A group of eight kobolds attacking the same PC each turn, while cultists keep other PCs away from the fray with spells and good positioning can be really dangerous.
5. Adjust the number of combat encounters
Combat encounters sequentially deplete party resources, and this is a big factor in their difficulty. Simply adding more encounters, even if using campaign-standard enemies for each, will stress party resources. This should be used sparingly-- maybe save it for a critical part of the adventure, rather than having every day work this way. Combat can slow the game down, and if each combat is easy a lot of encounters might become boring pretty quickly for you and your players.
6. Adjust availability of rests
A fully-rested party of PCs will essentially always punch above its weight, encounter-wise. A standard adventuring day forces them to be more cautious with their resources (who knows how many more combat encounters there will be before the next chance to rest?), and also means that with each additional fight they have fewer resources left to use. Five easy combats for a fully rested party might be two easy, two moderate, and one deadly encounter if they occur in sequence with no chance for recovering spell slots and class features in between.
7. Give less impressive rewards at the beginning
Some of this is taken care of through the XP scaling needed to get from level to level, but you can also award less XP than normal for encounters that aren't very challenging. It's not my favorite (players might be disappointed with their early rewards), but slowing the "planned" progression through the early phase of the campaign will eventually cause the party's PC level to converge on the campaign's expected level at that point, and then no more rebalancing would be necessary at all.
You can (and perhaps should) also restrict access to magic items, which often become available to players around level 4. This alone won't make encounters harder, but it will stop them from becoming even easier until the campaign "catches up" with your PCs.