Yes, you can take higher-level Stances at your first class level

There are several issues here.

First of all, this line is in the form of a descriptive statement, not a prescriptive one: it describes the usual case of things, rather than defining a limitation on your options. I would argue that it is there solely to help players new to the book, who are creating their first martial adept from level 1.

After all, a great many statements are made in Wizards’ products that assume you are single-classed, and starting from ECL 1 is the default assumption for the game. The Wizard’s Specialization feature says you cannot cast spells from your banned schools – but you actually can, you just need to get that ability from another class.

In addition, the line does not say “first-level martial adepts are restricted to 1st-level Stances.” It says that they “begin play” with a single 1st-level maneuver. A multiclass character taking his first level in a martial adept class after ECL 1 is not “begin[ning] play,” so the statement does not apply to him.

For that matter, taken literally, that would imply that any martial adept has only a single 1st-level Stance when the game starts – even if he started at level 20 and took Martial Stance feats repeatedly. Clearly, this is not the case, which is only further evidence that the line is not a rule, but a hint or (supposedly) helpful description.

Finally, if you rule that it does prevent higher-level Stances from being taken for your first class level, it flies in the face of the entire Tome of Battle design pattern. Tome of Battle was intentionally designed to mesh well with previous books and existing characters – that is why the Initiator Level rules were written the way they were in the first place.

Every single other method of learning any maneuvers – Stances included – allows those with higher Initiator Level to “skip” lower-level maneuvers – because Wizards finally understood how important it was to the system that characters be getting level appropriate class features, even if they multiclass. For instance, a 12th-level character, with no martial adept levels, still has an Initiator Level of 6, and can take Martial Study or Martial Stance to get a 3rd-level maneuver or stance, respectively.

This single supposed exception does not make any sense in light of the context that Tome of Battle provides, does not have the form of a prescriptive rule, and does not actually specify your first martial adept level but rather whether or not the character is “beginning play,” which really does not make much sense if taken literally.

Your initiator level does NOT determine what maneuvers you learn. Rather, they determine the maximum maneuver level for the purpose of multiclassing. The maneuver system has a cap on the number of maneuvers you know and can ready. The quantity and level of maneuvers you can learn and ready is entirely determined by whatever classes or feats you gain. If a feat says "you learn two 1st level maneuvers and can ready one of them," it means exactly that.

I will explain the feat in more detail.

1. You select one martial discipline and gain its associated skill as a class skill.
2. You gain an initiator level equal to 1/2 your character level + your initiation modifier (which you choose from your Int, Wis, or Cha modifier). This level cannot exceed your character level, as per Initiator Level errata on page 26. This initiator level applies to all maneuvers you gained through the Martial Training feats.
3. You learn two 1st level maneuvers from your discipline. The maneuver system does not allow you to learn additional maneuvers unless you take more Martial Training feats or gain a level in a martial disciple class (a class that has the "maneuvers readied" class feature).
4. You can ready only one maneuver you know.
5. You can spend a full-round action to recover a used maneuever.