At first is used for contrast, whereas just first is for describing a series of actions. Since at first usually contrasts initial thoughts, opinions, feelings, intentions, circumstances, etc. with some later result, it has to go along with past or future tenses. I think these initial states would all be described with imperfective verbs in Russian, too (is that right? [edit: now that I'm later in the tree I'm thinking that might have been an incorrect supposition...I'm still curious as to how this type of expression would map into Russian.]), where «найти» here is perfective. For example,
- I thought it would be bad at first, but then I tried it.
- At first she was afraid (she was petrified), but she knew she would survive. :D
- At first I was going to go to the store until I realized I had more in the cupboard.
- You'll feel a pinch at first (but it will be over quickly).
- They were paid very little at first until someone spoke up.
I'm not sure if I'm adding to your answer or just making things less clear for others. But in an attempt to clarify for myself:
(Disclaimer: I'm a monolingual native English speaker and thus bad at actually explaining my own native language or knowing what the word forms actually are).
It seems like, here at least, "Сначала" is more like an adverb much like the archaic "Firstly" or the slightly more used "At first".
If the phrase wanted a verb like "To begin with" (and I have no idea if this is even a phrase in Russian) then wouldn't you likely use начинать or начать? Obviously "Сначала" shares a root with those but seems to have a different meaning.
Right? Or no?
My native language is also not Russian, but I know this much: the prefix "с-" means something like "from" or "off" so it "сначала" literally means something like "from the start." I new believe that "to begin with" is best translated as "во-первых." I'm not so sure that you would use a verb for that.
Сначала can also mean "from the very beginning, anew, again" when used as an adverb. В начале cannot.
В начале ("at the beginning") can be further expanded with words saying the beginning of what you are talking about—and this is what you typically mean (в начале would be used if you mean "at the beginning" of something you have in mind).
Or the hint is wrong. I've found many cases where I was certain the hints were right and should be accepted. But I've also found many (based on comments and looking things up) where the hints bore no resemblance to the meaning of the sentence.
Not saying you're wrong ("To start with" here seems like it should be OK), just saying - just because it says it in the hint doesn't mean it's acceptable. This is still in beta and the hint could very well be wrong.
The hints include translations that may be appropriate for other uses of the word or phrase, not necessarily in this exercise. Many times, you will get more exposure later that will expand on or further clarify how the word is used. Keep in mind, though, that Russian is not simply English with a different vocabulary and alphabet. Some ideas/concepts are better understood intuitively, after many different examples. IME, it also helps to learn some etymology sometimes. You learn roots and why phrases are constructed the way they are, information that can help you figure out unfamiliar, but similar phrases.
Keep in mind, though, that Russian is not simply English with a different vocabulary and alphabet
I'm well aware of this and the more I learn, the more this becomes critically clear. But you absolutely make a good point.
You learn roots and why phrases are constructed the way they are
This is exactly what brought me to Russian. While it makes sense to, I have less interest in becoming conversational and more interest in the morphology. It's fascinating and, if I may (and related to your earlier point), almost poetic. Not to necessarily glorify it but, because it is so different from English, it requires a somewhat creative, tangential approach when evaluating word and phrase construction.