From an interview with the author, we know precisely when Shoko started liking Shoya. It is contained in the first collector's volume on page 738.
At this point, when she couldn't see Shoya for two weeks, Shoko realizes for the first time she has feelings for him. [...] Some people think Shoko tells Shoya she loves him in reaction to Naoka's presence, but it came about because of the two weeks when Shoko couldn't see Shoya at the bridge, and the fact that her hearing had worsened. These intensified her emotional state.
We don't get to see Shoko's thoughts and feelings about anything; this is an important theme of the story. We get other characters' perspectives and thus we can be relatively certain of what they're thinking, but we only get to see Shoko through the lens of these viewpoint characters. Even when the story is told through Shoko's perspective later on, it is murky and jumbled, making it hard to understand exactly what she's thinking. Thus, we can only ascertain how she initially felt about Shoya through her actions and by what she says.
With this in mind, I believe there is enough evidence to indicate she did not initially have romantic feelings towards Shoya. Firstly, let us keep in mind that Shoko is not an oblivious idiot, as Shoya first suspected (see page 95 of first volume). When Shoko asks Shoya for Miyoko's contact info, it becomes apparent to both Shoya and readers that Shoko is acutely aware of what was going on.
Shoko's Reaction When Shoya Appears Again
At the beginning of Volume 2, we see that Shoko's initial reaction to Shoya reappearing in her life is to run away. She decides to hear him out after he trips, but her expressions throughout the chapter seem to indicate displeasure or perhaps uncertainty), at least until Shoya shows that he knows sign language. This doesn't tell us how she initially felt about him, but it does tell us that at the end of their time together in elementary school, she didn't like him.
Shoko's Initial Reaction to Shoya
Just from reading Shoya's facial expressions, it seems that Shoko grows to distrust Shoya, and perhaps even to dislike him. In greeting, she gives Shoya the same cheery smile she gives everyone else, but this soon changes. In Chapter 2: Just One Of Those Things, there are three interactions (identical in terms of structure) between Shoko and Shoya on pages 75, 81, and 83. In each one, Shoko's expression becomes more and more wary. In the final one, her eyebrows slant downward ever so slightly when she notices Shoya, perhaps conveying a hint of anger. And this is all before Shoya begins his bullying in earnest. Getting told not to sing, having dust poured on her, and getting her hearing aids thrown out windows is unlikely to make Shoko develop a crush on Shoya. The normal reaction to such incidents would be a growing fear or hatred of the perpetrator.
This was not the first time Shoko was bullied, and she caught on very quickly to Shoya's mockery. Far from having a crush on Shoya, I think we can conclude that Shoko didn't like him.
Shoko Asks to Be Friends
There is an incident, just after Shoya injures Shoko by pulling on the apparatus in her right ear, where Shoko uses sign language to ask to be friends. This might be a singular piece of evidence supporting the idea that Shoko has a crush on Shoya, however, the timing doesn't really make sense for this; getting injured as she did should make this a low point in their relationship. But this incident can also be interpreted another way. Initially, Shoko apologizes to Shoya with her notebook, even though Shoya should be the one apologizing to her. This may just be Shoko's attempt to resolve her bullying situation. Her initial apology might indicate Shoko thinks she did something to upset Shoya, and this is why he's bullying her. In this desperate attempt, Shoko hopes to make amends and become friends so she won't be bullied anymore.
After Shoya Starts Getting Bullied
Which brings us to the point where Shoya starts getting bullied and why Shoko tried to help him. As previously stated, Shoko was aware of what was happening. She also blamed herself (we see Yuzuru speculate on this in Volume 2, page 138). She knew that her presence and her disability created a disruption in the class. Just as in the case of Miyoko, Shoko blamed herself for the bullying that happened to Shoya, and this is why she cleans off the messages on his desk, and why she tries to make things right by helping him out.
Later in the series, Naoka comments on how boys pick on girls they like, speaking as though this proves Shoko liked Shoya in elementary school, but I believe this reflects more on Naoka's jealousy than it does on how Shoko felt about the situation. I think it is reasonable to assume that Shoko disliked Shoya in elementary school, and that she only grew to like him after seeing the effort he made to correct his past mistakes.
All references are to Kodansha Comic's English version of the manga.