A pre-approval already in hand beats a financing condition left open-ended, since a seller weighing two similar offers will favour the one with less uncertainty attached. A larger deposit held in trust signals the same thing: a buyer who intends to close, not one testing the market.
Possession date flexibility is frequently the tiebreaker, since a buyer willing to match a seller's preferred move date at little cost to themselves reads as easier to deal with than one demanding an inconvenient one. A shorter, clearly scheduled home inspection condition, typically covering a $400 to $600 inspection, also signals seriousness over a vague one left open to the last day.
Price gets the offer noticed; the rest of the terms get it accepted. Get your hand-reviewed valuation from Joel Dyck.