No you cannot.
Cards and effects cannot be activated unless they are common knowledge. This means any face-up card on the field or in the graveyard (noted as GY on more recent cards), however cards in hand card be activated as well but these say you either need to discard the card (like Ash Blossom and Joyous Spring) or reveal it to your opponent (like Trickstar Lycoris).
So as Maiden is not common knowledge while face down so the effect cannot be activated as it "misses timing" which I will explain a bit more on.
This next part is a bit more general so I will use generic examples.
During the battle phase there is something known as the Battle step during this there are multiple sub-steps;
- Attack Declaration
- Damage Step
- Damage Calculation
This step is kind of self explanatory to what it means, it is the point in which the turn player declares their attack on a monster, at this point you can respond with certain cards like Mirror Force which has a specific activation requirement of an attack declaration.
When an opponent's monster declares an attack: Destroy all monsters
your opponent's attack position monsters.
Note: any other traps/quick-play spells/monsters using quick effects can still be activated at this point providing it is a legal play.
The damage step works slightly differently so bare with me if I am not clear. The damage step begins when both players have agreed to proceed after attack declaration, to put it simply at this point you can only activate Attack/Defense modifiers or cards that negate activations however other things can be activated too which I will get on to soon.
Attack modifier example Rush Recklessly
Target 1 face-up monster on the field; it gains 700 ATK until the end of this turn.
Negate activation example Solemn Judgement
When a monster would be Summoned, OR a Spell/Trap card is activated: Pay half your Life Points; negate the Summon or activation, and if you do, destroy that card.
Notice how it says activations.
This happens when both players have finished activating any cards in the damage step before the attack goes through so at this point is when the attack actually takes place and damage is dealt(if any), however this is still part of the damage step.
Earlier how I said other cards can be activated in the damage step, this is this point, these effects are cards that trigger if they are destroyed by battle (something like Sangan) or if it destroys something by battle (something like Sky Striker Mecharmory - Hercules Base) these still count as triggering in the damage step so cards like Ash blossom (which I mentioned earlier) cannot be activated in response as Ash negates effects not activations but however Solemn Judgement can be activated in response to these.
Back to Maiden
So if we go back to the example of Maiden with Eyes of Blue in face down. Monsters are not flipped face up when attacked until the Damage Step which is after Attack Declaration (so Maiden has missed timing which is a phrase I mentioned earlier), so by then using the steps I provided you can see why Maiden cannot be activated even in the damage step.