The word "off" in "off to a great start" is part of an idiom and as such does not have a literal dictionary meaning. However, without a careful examination of the language, one might choose your first dictionary definition:
From a place or position: He walked off in a huff.
That agrees with your own analogy:
If an aircraft, bird, or insect takes off, it leaves the ground and
begins to fly
First Dictionary Definition
The problem with your first dictionary definition is that it applies to a physical movement, i.e. walking, away from a defined starting point. Not all "great starts" or beginnings are a physical movement, as I am sure we all know. The example in your question is of taking an online course, which requires very little physical movement. At the same time, it is a mental or figurative, i.e. abstract, move forward from a defined starting point. That starting point would most likely have been your online registration for the course--again requiring a minimum of physical movement.
Levels of Physical Movement
To emphasize these levels of physical movement across a variety of new beginnings many people encounter, I composed a list of other things on which one could be "off to a great start." Some of these actions are physical and begin from a physically defined starting point, while some are metaphorical or abstract and begin from a socially constructed, i.e. abstract or figurative, starting point as shown below:
- a foot race, a journey by land, sea, or air
- life in a new country, a new construction project, or a new job
- an academic paper, marriage, a promotion at work
Though I cannot reference these "levels of physical movement," since I base them on my own observation of life and my experience with the English language, I am sure the difference will become clear to the reader.
Category 1 is the most literal physical movement away from clearly defined starting points; there is no need to name these points.
Category 2 is somewhat more abstract because life in a new country is a continuation of one's personal life; a new construction project is a continuation of one's vocation as a construction worker; a new job is just another means of earning an income. At the same time, there are dates and physical points of departure to mark the new beginnings.
Category 3 is abstract and depends on social constructs or rituals that:
- change a batch of words from "notes" into an "academic paper."
- change the legal status of a relationship between two human beings.
- change one's status within the organization.
Clearly, starting an online course falls into Category 3, the category of socially constructed abstract beginnings; it is not physical as in "He walked off in a huff." This is why I reject your first dictionary definition.
To encourage is an example of Category 3 Level of Physical Movement.
Regarding the meaning of "off" in "off to a great start," you say:
I understand it is some kind of encouragement, similar to "well done".
Having myself now been immersed for about twenty years in a culture that uses this idiom, I agree. I think all cultures know the value of a positive evaluation of the initial performance and that encouragement at this point can give the person strength to persevere through difficult times ahead. It means "well done." However, encouragement is abstract; it is not a literal or physical action.
What Constitutes an Idiom?
This brings us back to my statement above that the word "off" in "off to a great start" is part of an idiom and as such does not have a literal dictionary meaning. If we adhere to the first dictionary meaning above, we will disagree. We might think "idiom" equals "idiot," i.e. nonsensical sentence fragment. It does not. An idiom is a well-established group of words that speakers of the English language understand within their context to mean something specific, other than the literal dictionary definitions of each word.
From Online Teachers UK:
An idiom is a phrase or group of words that, when taken together, has
a meaning that is different from that of each individual word. To put
it another way: idioms cannot be understood literally.
That agrees with Scholastic Teaching Resources, Idiomatic Expressions, which states:
An idiom is a phrase or expression whose meaning can't be understood
from the ordinary meanings of the words in it. For example, "Get off
my back!" is an idiom meaning "Stop bothering me!" The idiom "You hit
the nail on the head" means "You're exactly right."
To examine the examples in this Scholastic quote:
Get off my back!
If someone has literally climbed onto my back, the words in that statement mean exactly what they say: You who are on my back, get off! However, it is also an idiom commonly used when one person is nagging or bothering another person. "Just stop, will you!" the frustrated person might exclaim. "Get off my back!" does not in this case mean the annoying person has physically climbed onto anyone's back.
You hit the nail on the head.
The same applies to "You hit the nail on the head." It can be a literal statement when people are hammering nails, but it is often used as an idiom to mean "You are exactly right."
To draw on the above Categories of Physical Action, it might therefore be said that an idiom is taking the level of physical action beyond Category 3. Again, I can't reference this, since it is based on observation and common sense, but I feel confident the reader will understand the intended meaning. "Off" in "off to a great start" must be taken in the context of the entire group of words to have meaning. At the risk of being redundant, the Farlex Dictionary of Idioms carries the same sentiment regarding "off to a good start":
Starting (something) in a very favorable or positive way.
After dropping out of college once before, I really want to get this second
chance off to a good start.
The project is off to a good start, but we need to make sure we keep up the pace.